Instituto Politcnico NacionalESCOMIntegrales de GranvilleTarea #7Materia:CalculoAlumno:Fernando Guerrero EspinosaGrupo:1cv8Fecha de Entrega10 de Julio del 2015

INTEGRALES RESUELTAS A MANO.

INTEGRALES EN MATLAB

PAGINA 238 EJERCICIO 28>> syms s t a>> S=(t^3)/(((a^4)+(t^4))^(1/2));int(S) ans =(a^4 + t^4)^(1/2)/2-----------------------------------EJERCICIO 29>> syms a t b y >> S=1/(a+b*y)^3;int(S)ans =-1/(2*a^2*b + 4*a*b^2*y + 2*b^3*y^2)------------------------------------EJERCICIO 30>> syms x a b>> S=x/(a+b*(x^2))^3;int(S)ans = -1/(4*a^2*b + 8*a*b^2*x^2 + 4*b^3*x^4)-------------------------------------EJERCICIO 31>> syms a b t>> S=(t^2)/(a+b*(t^3))^2;int(S)ans =-1/(3*b*(b*t^3 + a))--------------------------------------EJERCICIO 32>> syms z a b>> S=(z)*((a+b*(z^3))^2);int(S)ans =(a^2*z^2)/2 + (2*a*b*z^5)/5 + (b^2*z^8)/8-----------------------------------------EJERCICIO 33>> syms x n a b>> S=(x^(n-1))*(a+b*(x^n))^(1/2);int(S)ans =(2*(a + b*x^n)^(3/2))/(3*b*n)-----------------------------------------EJERCICIO 34>> syms x>> S=(2*x+3)/((x^2)+3*x)^(1/2);int(S)ans =2*(x*(x + 3))^(1/2)------------------------------------------EJERCICIO 35>> syms x>> S=(3*((x^2)+1))/((x^3)+3*x)^(1/2);int(S)ans =2*(x^3 + 3*x)^(1/2)-----------------------------------------EJERCICIO 36

>> syms x log>> S=(2+log x)/(x);int (S)-----------------------------------------EJERCICIO 37

38.__________

>> S=(sin(a*x))*(cos(a*x));>> int(S) ans = -cos(2*a*x)/(4*a)

39.__________

>> S=(sin(2*x))*(cos(2*x)^2);>> int(S) ans = -(2*cos(x)^2 - 1)^3/6

40.__________

>> S=(tan(x/2))*(sec(x/2)^2);>> int(S) ans = tan(x/2)^2

41.__________

>> S=(cos(a*x))/(b+sin(a*x))^(1/2);>> int(S) ans = (2*(b + sin(a*x))^(1/2))/a

42.__________

>> S=((sec(x))/(1+tan(x)))^2;>> int(S) ans = -1/(tan(x) + 1)

43.__________

>> S=1/(2+3*x);>> int(S) ans = log(x + 2/3)/3

44.__________

>> S=(2*(x^2))/(2+(x^3));>> int(S) ans = (2*log(x^3 + 2))/3

45.__________

>> S=t/(a+b*(t^2));>> int(S) ans = log(b*t^2 + a)/(2*b)

46.__________

>> S=(2*x+3)/((x^2)+3*x);>> int(S) ans = log(x*(x + 3))

47.__________

>> S=(2*(y+2))/((y^2)+4*y);>> int(S) ans = log(y*(y + 4))---------------------------Pgina 239, ejercicio 48syms theta a b expy=(exp^(theta))/(a+(b*exp^(theta)))int(y,theta)

Pgina 239, ejercicio 49syms xy=(sin(x))/(1-cos(x))int(y,x)

Pgina 239, ejercicio 50syms y a bf=(sec(y))^2/(a+b*tan(y))int(f,y)

Pgina 239, ejercicio 51syms xy=((2*x)+3)/(x+2)int(y,x)

Pgina 239, ejercicio 52syms xy=((x^2)+2)/(x+1)int(y,x)

Pgina 239, ejercicio 53syms xy=(x+4)/(2*x+3)int(y,x)

Pgina 239, ejercicio 54syms sy=(exp^(2*s))/(exp^(2*s)+1)int(y,s)

Pgina 239, ejercicio 55syms a exp theta by=(a*(exp^theta)+b)/(a*(exp^theta)-b)int(y,theta)

Pgina 239, ejercicio 56syms xy=2*x/(6-5*x^2)^(1/3)int(y,x)

Pgina 239, ejercicio 57syms xy=(x^3)+(3*x^2)int(y,x)

Pgina 239, ejercicio 58syms xy=((x^2)-4)/(x^4)int(y,x)

------------------------Pgina 239, ejercicio 59>>syms xy=((5*x)^(1/2)/5)+(5/(5*x)^(1/2));>>int(y)

ans =

5^(1/2)*x^(1/2)*((2*x)/15 + 2)------------------------------------------------------------------------------------------Ejercicio 60>>syms bdyy=b*(y^2)^(1/3);>>int(y)

ans =

int(b*((5/(5*x)^(1/2) + (5*x)^(1/2)/5)^2)^(1/3), x)-------------------------------------------------------------------------------------------------Ejercicio 61>>syms ty=1/(t*((2*t)^(1/2)));>>int(y)

ans =

-2^(1/2)/t^(1/2) -------------------------------------------------------------------------------------------------Ejercicio 62>>syms x>> y=(2-3*x)^(1/3);>>int(y)

ans =

-(2 - 3*x)^(4/3)/4-------------------------------------------------------------------------------------------------Pgina 249, ejercicio 13>>syms a>> y=a*x/(x^4+b^4);>>int(y)

ans =

(a*atan(x^2/b^2))/(2*b^2)----------------------------------------------------------------------------------------------------Ejercicio 14>>syms t>> y=1/((t-2)^2+9);>>int(y)

ans =

atan(t/3 - 2/3)/3---------------------------------------------------------------------------------------------------Ejercicio 15>>syms y>> y=1/(1+(a^2)*(y^2))^(1/2);>>int(y)

ans =

asinh(y*(a^2)^(1/2))/(a^2)^(1/2)--------------------------------------------------------------------------------------------------------Ejercicio 16>>syms u>> y=1/((4-(u+3)^2)^1/2);>>int (y)

ans =

atanh(u/2 + 3/2)-----------------------------------------------------------------------------------------------------------Ejercicio 17>>syms x>> y=1/(9-16*(x^2))^(1/2);>>int(y)

ans =

asin((4*x)/3)/4------------------------------------------------------------------------------------------------------------------Ejercicio 18>>syms y>> y=1/(9*(y^2)+4)^(1/2);>>int(y)

ans =

asinh((3*y)/2)/3-----------Pgina 249, ejercicio 19syms tY=1/(4*(t^2)+25);int(Y)ans =atan((2*t)/5)/10

------------------------------------------------------------------------------------------Ejercicio 20syms xy=1/(25*(x^2)-4);int(Y)ans = -atanh((5*x)/2)/10

-------------------------------------------------------------------------------------------------Ejercicio 21syms x Y=7/(3+7*(x^2));int(Y)ans =(21^(1/2)*atan((21^(1/2)*x)/3))/3-------------------------------------------------------------------------------------------------Ejercicio 22syms xy=3/(9*(y^2)-16);int(y)Ans =-atanh((3*y)/4)/4

-------------------------------------------------------------------------------------------------Ejercicio 23syms xy=1/(4*(Y^2)+5)^(1/2);int(y)ans = asinh((2*5^(1/2)*y)/5)/2----------------------------------------------------------------------------------------------------Ejercicio 24syms ty=t/((t^2)-4)^(1/2);int(y)ans = (t^2 - 4)^(1/2)---------------------------------------------------------------------------------------------------Ejercicio 25syms xy=x/(5*(x^2)+3)^(1/2); int(y)ans = (5^(1/2)*(x^2 + 3/5)^(1/2))/5

--------------------------------------------------------------------------------------------------------Ejercicio 26syms xy=(2*exp(x))/(1-exp(2*x))^(1/2);int(y)ans = 2*asin(exp(x))-----------------------------------------------------------------------------------------------------------Ejercicio 27syms yy=(6*t)/(8-3*(t^2)); int(y)ans = -log(t^2 - 8/3)

------------------------------------------------------------------------------------------------------------------Ejercicio 28syms xy=(sin(x))/(4+(cos(x))^2)^(1/2);int(y)ans = -asinh(cos(x)/2)

----------Pagina 249

Ejercicio 29

syms x y m ny = 1/(m^2+((x+n)^2))int(y,x)y = atan((n + x)/m)/mdiff(y,x)

Ejercicio 30

syms u yy = 1/(4-(((2*u)-1)^2))int(y,u)y = atanh(u - 1/2)/4diff(y,u)

Ejercicio 31

syms x yy = ((7*((x)^2)))/(5-((x)^6))int(y,x)y = (7*5^(1/2)*atanh((5^(1/2)*x^3)/5))/15diff(y,x)

Pagina 251

Ejercicio 7

syms y xy = 1/(sqrt((15)+(2*x)-((x)^2)))int(y,x)

Ejercicio 8

syms y xy = 1/((x^2)+(2*x))int(y,x)

Ejercicio 9

syms y xy = 1/((4*x)-(x^2))int(y,x)

Ejercicio 10

syms y x y = 1/(sqrt((2*x)-(x^2)))int(y,x)

Ejercicio 11

syms y s ay = 1/(sqrt((2*(a*s))+(s^2)))int(y,s)

Ejercicio 12

syms y1 yy1 = 1/((y^2)+(3*y)+(1))int(y1,y)

Ejercicio 13

syms y xy = 1/((1)+(x)+(x^2))int(y,x)------------Pgina 251:

-Ejercicio 14

>> syms xy=1/((1+x+x^2)^(1/2))int(y,x) y = 1/(x^2 + x + 1)^(1/2) ans = log(x + (x^2 + x + 1)^(1/2) + 1/2)

-Ejercicio 15

>> syms xy=1/(4*x^2+4*x+5)int (y,x) y = 1/(4*x^2 + 4*x + 5)

ans = atan(x + 1/2)/4

-Ejercicio 16

>> syms x>> y=1/(3*x^2-2*x+4) y = 1/(3*x^2 - 2*x + 4) >> int (y,x) ans = (11^(1/2)*atan((11^(1/2)*(3*x - 1))/11))/11

-Ejercicio 17

>> syms xy=1/((2-3*x-4*x^2)^(1/2))int (y,x) y = 1/(- 4*x^2 - 3*x + 2)^(1/2) ans = asin((41^(1/2)*(8*x + 3))/41)/2

-Ejercicio 18

syms xy=1/(x^2+2*x+10)int (y,x) y = 1/(x^2 + 2*x + 10) ans = atan(x/3 + 1/3)/3

-Ejercicio 18

>> syms xy=1/(x^2+2*x-3)int (y,x) y = 1/(x^2 + 2*x - 3) ans = -atanh(x/2 + 1/2)/2

-Ejercicio 19

>> syms xy=1/(x^2+2*x-3)int (y,x) y = 1/(x^2 + 2*x - 3) ans = -atanh(x/2 + 1/2)/2

-Ejercico 20

>> syms y xy=1/(3-2*y-y^2)int (y) y = -1/(y^2 + 2*y - 3) ans = atanh(y/2 + 1/2)/2

-Ejercicio 21

syms y uy=3/((5-4*u-u^2)^(1/2))int (y, u) y = 3/(- u^2 - 4*u + 5)^(1/2) ans = 3*asin(u/3 + 2/3)

-Ejercicio 22

>> syms y xy=5/((x^2+2*x+5)^(1/2))int (y, x) y = 5/(x^2 + 2*x + 5)^(1/2) ans = 5*log(x + (x^2 + 2*x + 5)^(1/2) + 1)

-Ejercicio 23

>> syms y xy=5/((x^2+4*x+3)^(1/2))int (y, x) y = 5/(x^2 + 4*x + 3)^(1/2) ans = 5*log(x + (x^2 + 4*x + 3)^(1/2) + 2)----Pagina 251 Ejercicio 24syms x a y=(1/(x.^2 + 2*x)^(1/2));int(y, x)ans =log(x + (x*(x + 2))^(1/2) + 1)

ejercicio 25

syms ty=(1/(3*t - 2*(t.^2))^(1/2));int(y, t)ans =(2^(1/2)*asin((4*t)/3 - 1))/2

Ejercicio 26syms xy=(1/(x.^2 - 4*(x)+5));int(y, x)ans =atan(x - 2)

Ejercicio 27syms xy=(1/(2 + 2*(x)-x.^2));int(y, x)ans =(3^(1/2)*atanh(3^(1/2)*(x/3 - 1/3)))/3

Ejercicio 28

syms ry=(1/(r.^2 - 2*(r)-3));int(y, r)ans =-atanh(r/2 - 1/2)/2

Ejercicio 29syms xy=(4/(x.^2 - 4*(x)+13)^(1/2));int(y, x)ans =4*log(x + (x^2 - 4*x + 13)^(1/2) - 2)

Pgina 253 Ejercicio 1syms xy=((1+2*x)/(1+x.^2));int(y, x)ans =log(x^2 + 1) + atan(x)

Ejercicio 2syms xy=((2*x+1)/sqrt((x.^2 - 1 )));int(y, x)ans =acosh(x) + 2*(x^2 - 1)^(1/2)

Ejercicio 3syms xy=((x-1)/sqrt(1-x.^2));int(y, x)ans =- asin(x) - (1 - x^2)^(1/2)

Ejercicio 4

syms xy=((3*x-1)/(x.^2 + 9));int(y, x)ans =(3*log(x^2 + 9))/2 - atan(x/3)/3--Pagina 253.Ejercicio 5

syms y sy = (((3*s)-2))/(sqrt(9-(s^2)))int (y,x)

Ejercicio 6

syms y xy = (x+3)/(sqrt((x^2)+4))int(y,x)

Ejercicio 7

syms x yy = ((2*x)-5)/((3*(x^2))-2)int(y,x)

Ejercicio 8

syms y ty = ((5*t)-1)/ ((3*(t^2))-9)^(1/2)int(y,t)

Ejercicio 9

syms y xy = (x+3)/((6*x)-x^2)int(y,x)

Ejercicio 10

syms x y y = (2*x)+5/((x^2)+(2*x)+5)int(y,x)

Ejercicio 11

syms x yy = (1-x)/(4*(x^2)-(4*x)-3)int (y,x)

Ejercicio 12

syms y xy = ((3*x)-2)/((1)-(6*x)-(9*(x^2)))int (y,x)

Ejercicio 13

syms x yy = (x+3)/((x^2)+(2*x))^(1/2)int(y,x)

Ejercicio 14

syms y xy = (x+2)/sqrt((4*x)-(x^2))int(y,x)--PAGINA 263

Ejercicio 11

>> syms x a>> y=((sec(a*x))/(tan(a*x)))^4;>> int(y,x) ans = -(cot(a*x)*(cot(a*x)^2 + 3))/(3*a)

Ejercicio 12

>> syms o>> y=((cot (2*o))^2)+((cot (2*o))^4)y =cot(2*o)^2 + cot(2*o)^4>> int(y)ans =-cot(2*o)^3/6

Ejercicio 13

>> syms t b>> y=((tan(b*t))-(cot(b*t)))^3y = -(cot(b*t) - tan(b*t))^3>> int(y)ans =(4*log(tan(b*t)) - 4*log(tan(b*t)^2 + 1) + 1/(2*tan(b*t)^2) + tan(b*t)^2/2)/b

Ejercicio 14

> syms x a>> y=(cot(a*x))^5y =cot(a*x)^5>> int(y)ans =- ((x*i)/4 - (x*(sin(2*a*x)^2 - 1)*i)/4 + (x*(2*sin(a*x)^2 - 1)*i)/2)/sin(a*x)^4 + (log(sin(2*a*x)*i - 2*sin(a*x)^2)/4 + sin(a*x)^2 - (log(sin(2*a*x)*i - 2*sin(a*x)^2)*(sin(2*a*x)^2 - 1))/4 + (log(sin(2*a*x)*i - 2*sin(a*x)^2)*(2*sin(a*x)^2 - 1))/2 - 1/4)/(a*sin(a*x)^4)

Ejercicio 15

>> syms o>> y=(sec(o))^6y =1/cos(o)^6>> int(y)ans =(3*sin(o) + 4*cos(o)^2*sin(o) + 8*cos(o)^4*sin(o))/(15*cos(o)^5)

Ejercicio 16

>> syms x>> y=(csc(x/2))^6y =1/sin(x/2)^6>> int(y)ans =-(2*(3*cos(x/2) + 4*cos(x/2)*sin(x/2)^2 + 8*cos(x/2)*sin(x/2)^4))/(15*sin(x/2)^5)

Ejercicio 17

>> syms t>> y=((sec(t))^4)/((tan(t))^3)y =1/(cos(t)^4*tan(t)^3)>> int(y)ans =log(tan(t)) - 1/(2*tan(t)^2)

Ejercicio 18

>> syms x>> y=((sec(x))^4)/((tan(x))^(1/2));>> int(y)ans =(4*sin(2*x)^(1/2)*(4*cos(x)^2 + 1))/(5*(2*cos(x)^2)^(3/2))

Ejercicio 19

>> syms x a>> y=((csc(a*x))/(cot(a*x)))^4 y = 1/(cot(a*x)^4*sin(a*x)^4) >> int(y) ans = (tan(a*x)*(tan(a*x)^2 + 3))/(3*a)

Ejercicio 20

>> syms x>> y=((tan(x/3))^3)*((sec(x/3))^3);>> int(y) ans = -(cos(x/3)^2 - 3/5)/cos(x/3)^5--pag 26321syms xy=( 1/((sin(3*x)).^(4))*((cos(3*x)).^(2)) );int(y)ans = -cot(3*x)^3/9

22>> syms x b >> y=( (csc(b*x)/tan(b*x)).^4);>> >> int(y) ans = -(cot(b*x)^5*(5*cot(b*x)^2 + 7))/(35*b)

23>> syms x>> y=( (tan(x)/cot(x)).^2);>> int(y) ans = x - tan(x) + tan(x)^3/3

24>> syms t a>> y=(tan(a*t)/cos(a*t))^4 y = tan(a*t)^4/cos(a*t)^4 >> int(y) ans = (tan(a*t)^5*(5*tan(a*t)^2 + 7))/(35*a)

25>> syms x

>> y=((tan(x)^3)/sqrt(sec(x)));>> int(y) ans = (6*cos(x)^2 + 2)/(3*cos(x)^2*(1/cos(x))^(1/2)) >>

27

>> syms xy=(((sin(3*x))^4)/((cos(3*x))^2) );int(y) ans = sin(3*x)/(3*cos(3*x)) - (3*x)/2 + (cos(3*x)*sin(3*x))/6

>>

pag 2736>> syms x >> y=( x*sin(3*x).^2);>> int(y) ans = sin(3*x)^2/36 - (x*sin(6*x))/12 + x^2/4

7>> syms x n

>> y=((x^2)*sin (n*x));>> int(y) ans = (2*x*sin(n*x))/n^2 - cos(n*x)*(x^2/n - 2/n^3) >>

8>> syms x ay=(x*a)^2;int(y) ans = (a^2*x^3)/3 >> --

Ejercicio 9>> syms x n>> y=(x^(n))*(log(x))y = x^n*log(x)>> int (y,x)ans = piecewise([n == -1, log(x)^2/2], [n ~= -1, (x^(n + 1)*(log(x)*(n + 1) - 1))/(n + 1)^2])Ejercicio 10>> syms x>> y=asin(x)y = asin(x)>> int (y,x)ans = x*asin(x) + (1 - x^2)^(1/2)Ejercicio 11>> syms x>> y= atan (x)y = atan(x)>> int (y,x)ans =x*atan(x) - log(x^2 + 1)/2Ejercicio 12>> syms z>> y= acot (z)y =acot(z)>> int (y,z)ans =log(z^2 + 1)/2 + z*acot(z)Ejercicio 13>> syms x>> y= acos(2*x)y =acos(2*x)>> int(y,x)ans =x*acos(2*x) - (1 - 4*x^2)^(1/2)/2Ejercicio 14>> syms x>> y= asec(x)y =acos(1/x)>> int (y,x)ans = x*acos(1/x) - acosh(x)*sign(x)Ejercicio 15>> syms t>> y= acsc (t/2)y = asin(2/t)>> int(y,x)ans = x*asin(2/t)Ejercicio 16>> syms x>> y=(x)*(atan(x))y =x*atan(x)>> int (y,x)ans = atan(x)*(x^2/2 + 1/2) - x/2Ejercicio 17>> syms x>> atan(x)^(1/2)ans = atan(x)^(1/2)>> int (y,x)ans = atan(x)*(x^2/2 + 1/2) - x/2Ejercicio 18>> syms x>> y=(x^(2))*(exp(x))y =x^2*exp(x)>> int (y,x)ans = exp(x)*(x^2 - 2*x + 2)%19 Pagina 273 syms thetay19=exp(theta)*(cos(theta))int(y19,theta)

%20 Pagina 273 syms xy20=(log(x))/((x+1)^2)int(y20,x)

%21 Pagina 273 syms xy21=(x^2)*(asin(x))int(y21,x)

%22 Pagina 273 syms xy22=(log(x+1))/(sqrt(x+1))int(y22,x)

%23 Pagina 273 syms xy23=(x*exp(x))/((1+x)^2)int(y23,x)

%24 Pagina 273 syms ty24=(exp(-t))*(cos(pi*t))int(y24,t)

%1 Pagina 275 syms xy1=(3*x)/(sqrt(5-(2*(x^2))))int(y1,x)

%2 Pagina 275 syms xy2=(3*x)/(5-(2*(x^2)))int(y2,x)

%3 Pagina 275 syms a b c xy3=((a*x)+b)/(sqrt((c^2)-(x^2)))int(y3,x)

%4 Pagina 275 syms xy4=(x)*(cos(2*x))int(y4,x)--Pagina 275 ejercicio 5syms xf=(4*x+3)/(x^2+4*x+8)int (f,x)ans= / x \ 5 atan| - + 1 | 2 \ 2 / 2 log(x + 4 x + 8) - --------------- 2------------------------------------------------------------------------Pagina 275 ejercicio 6

syms xf=(4*x+3)/sqrt((x^2+4*x+8))int (f,x)

ans= 2 1/2 2 1/2 4 (x + 4 x + 8) - 5 log(x + (x + 4 x + 8) + 2)------------------------------------------------------------------------Pagina 275 ejercicio 7

syms x af=1/((a^2 - x^2)^(3/2))int (f,x)

ans= x --------------- 2 2 2 1/2 a (a - x )-------------------------------------------------------------------------Pagina 275 ejercicio 8

syms xf=1/(x^2-6*x+9)int (f,x)

ans= 1 - ----- x - 3-------------------------------------------------------------------------Pagina 275 ejercicio 9

syms x f=1/(x^2-6*x+8)int (f,x)

nas=-atanh(x - 3)--------------------------------------------------------------------------Pagina 275 ejercicio 10

syms x f=1/(x^2-6*x+10)int (f,x)

ans=atan(x - 3)--------------------------------------------------------------------------Pagina 275 ejercicio 11

syms x ef=((e^(2*x)+(2*e)^-x))^2int (f,x)

ans=e^(4*x)/(4*log(e)) - (2/2^x*e^x)/(log(2) - log(e)) - 1/2^(2*x)/(2*e^(2*x)*(log(2) + log(e)))--------------------------------------------------------------------------Pagina 275 ejercicio 12

syms x ef=(e^(2*x)-(2*x))^2int (f,x)

ans=(e^(2*x) - log(e)*(2*e^(2*x)*x - e^(4*x)/4))/log(e)^2 + (4*x^3)/3----------------------------------------------------------------------------Pagina 275 ejercicio 13

syms x ef=1/(e^x)-((4*e)^-x)int (f,x)

ans=1/2^(2*x)/(e^x*(2*log(2) + log(e))) - 1/(e^x*log(e))-----------------------------------------------------------------------------Pagina 275 ejercicio 14

syms x af=(sin(a*x)*sin(a*x))*(cos(a*x))int (f,x)

ans=sin(a*x)^3/(3*a)--Pgina 249, ejercicio 19syms tY=1/(4*(t^2)+25);int(Y)ans =atan((2*t)/5)/10

------------------------------------------------------------------------------------------Ejercicio 20syms xy=1/(25*(x^2)-4);int(Y)ans = -atanh((5*x)/2)/10

-------------------------------------------------------------------------------------------------Ejercicio 21syms x Y=7/(3+7*(x^2));int(Y)ans =(21^(1/2)*atan((21^(1/2)*x)/3))/3-------------------------------------------------------------------------------------------------Ejercicio 22syms xy=3/(9*(y^2)-16);int(y)Ans =-atanh((3*y)/4)/4

-------------------------------------------------------------------------------------------------Ejercicio 23syms xy=1/(4*(Y^2)+5)^(1/2);int(y)ans = asinh((2*5^(1/2)*y)/5)/2----------------------------------------------------------------------------------------------------Ejercicio 24syms ty=t/((t^2)-4)^(1/2);int(y)ans = (t^2 - 4)^(1/2)---------------------------------------------------------------------------------------------------Ejercicio 25syms xy=x/(5*(x^2)+3)^(1/2); int(y)ans = (5^(1/2)*(x^2 + 3/5)^(1/2))/5

--------------------------------------------------------------------------------------------------------Ejercicio 26syms xy=(2*exp(x))/(1-exp(2*x))^(1/2);int(y)ans = 2*asin(exp(x))-----------------------------------------------------------------------------------------------------------Ejercicio 27syms yy=(6*t)/(8-3*(t^2)); int(y)ans = -log(t^2 - 8/3)

------------------------------------------------------------------------------------------------------------------Ejercicio 28syms xy=(sin(x))/(4+(cos(x))^2)^(1/2);int(y)ans = -asinh(cos(x)/2)

--Pagina 275, ejercicio 25

>> syms t>> f=(sin(t/4))^5;>> int(f) ans = -(4*cos(t/4)*(3*cos(t/4)^4 - 10*cos(t/4)^2 + 15))/15---------------------------------------------------------------------------ejercicio 26

>> syms t>> f=(sin(t/5))^4;>> int(f) ans = (3*t)/8 - (5*sin((2*t)/5))/4 + (5*sin((4*t)/5))/32---------------------------------------------------------------------------ejercicio 27

>> syms t>> f=(t-(csc(2*t)^2))/((t^2)+(cot(2*t)));>> int(f) ans = int((t - 1/sin(2*t)^2)/(cot(2*t) + t^2), t)---------------------------------------------------------------------------ejercicio 28

>> syms x>> f=((asin(x))/(1-(x^2)))^(1/2);>> int(f) ans = (2*asin(x)*(1 - x^2)^(1/2)*(-asin(x)/(x^2 - 1))^(1/2))/3---------------------------------------------------------------------------ejercicio 29

>> syms x>> f=(5/((x^2)-x+1));>> int(f) ans = (10*3^(1/2)*atan((3^(1/2)*(2*x - 1))/3))/3---------------------------------------------------------------------------ejercicio 30

>> syms x>> f=(5/(((x^2)-x+1)^(1/2)));>> int(f) ans = 5*log(x + (x^2 - x + 1)^(1/2) - 1/2)---------------------------------------------------------------------------ejercicio 31

>> syms x>> f=((x^3)*atan(x/2));>> int(f) ans = 2*x - 4*atan(x/2) + (x^4*atan(x/2))/4 - x^3/6---------------------------------------------------------------------------ejercicio 32

>> syms x>> f=((exp(x))+sin(x))^2;>> int(f) ans = x/2 + exp(2*x)/2 - exp(x)*cos(x) - (cos(x)*sin(x))/2 + exp(x)*sin(x)---------------------------------------------------------------------------Pagina 360, ejercicio 5

>> syms x>> f=(x-18)/((4*(x^3))+(9*x));>> int(f) ans = log(x - (3*i)/2)*(1 - i/12) + log(x + (3*i)/2)*(1 + i/12) - 2*log(x)---------------------------------------------------------------------------ejercicio 6

>> syms y>> f=((2*(y^3))+(y^2)+(2*y)+2)/((y^4)+(3*(y^2))+2);>> int(f) ans = log(y^2 + 2) + atan(y)--Pagina 360 Ejercicio 7>> syms y z y= (1/(z.^4+z.^2)); int(y,z) ans = - atan(z) - 1/z

Pagina 360 Ejercicio 8>> syms x y y=(2*x/((x.^2+1)*(x+1).^2)); int(y) ans = atan(x) + 1/(x + 1)

Pagina 360 Ejercicio 9>> syms x y=(x.^3+3*x)/((x.^2+1).^2); int(y) ans = log(x^2 + 1)/2 - 1/(x^2 + 1)

Pagina 360 Ejercicio 10>> syms x y= ((x^5+9*x^3-9*x^2-9)/(x^3+9*x)); int(y) ans =x^3/3 - log(x*(x^2 + 9)^4)

Pagina 360 Ejercicio 11 ***>> syms x y= ((4*x.^2+2*x+8)/(x*(x.^2+2).^2)); int(y) ans =2*log(x) + x/(2*(x^2 + 2)) - log(x - 2^(1/2)*1i)*((2^(1/2)*1i)/8 + 1) + log(x + 2^(1/2)*1i)*((2^(1/2)*1i)/8 - 1)

Pagina 360 Ejercicio 12>> syms t y=((t.^5)/((t.^2+4).^2)); int(y) ans =t^2/2 - 8/(t^2 + 4) - 4*log(t^2 + 4)

Pagina 360 Ejercicio 13>> syms x y=(1/(x.^3+x.^2+x)); int(y) ans =log(x) + log(x - (3^(1/2)*1i)/2 + 1/2)*((3^(1/2)*1i)/6 - 1/2) - log(x + (3^(1/2)*1i)/2 + 1/2)*((3^(1/2)*1i)/6 + 1/2)

Pagina 360 Ejercicio 14>> syms x y=((x.^5+4*x^3)/((x^2+2)^3)); int(y) ans =log(x^2 + 2)/2 + 1/(x^4 + 4*x^2 + 4)

Pagina 360 Ejercicio 15>> syms x y=(4/(x^4-1)); int(y) ans = - 2*atan(x) - 2*atanh(x)

Pagina 360 Ejercicio 16>> syms z y=((2*z.^2+3*z+2)/((z+2)*(z^2+2*z+2))); int(y) ans =2*log(z + 2) + atan(17/(2*(8*z + 6)) + 1/4)

--pagina_360_ejercicio_17 >> syms t y>> y=(((t+3)/(t.^2+4*t+5)).^2);>> int(y,t) ans =atan(t + 2) - 1/(t^2 + 4*t + 5)

pagina_360_ejercicio_18>> syms x y>> y=((5*x.^2+4)/(x.^3+4*x));>> int(y,x,1,4) ans = log(64)

pagina_360_ejercicio_19>> syms x y>> y=((5*x)/((x+2)*(x.^2+1)));>> int(y,x,0,1) ans = pi/4 + log(8/9)

pagina_360_ejercicio_20>> syms x y>> y=((2*x.^2+x+3)/((x+1)*(x.^2+1)));>> int(y,x,0,1) ans = pi/4 + log(4)

pagina_360_ejercicio_21>> syms x y>> y= ((4*x.^2+2*x)/((x.^2+1)*(x+1).^2));>> int(y,x,0,1) ans = pi/4 - log(2) + 1/2

pagina_360_ejercicio_23>> syms y z>> y=((z.^3+2*z.^2+6*z+8)/(z.^2+4).^2);>> int(y,z,0,2) ans = pi/4 + log(2)/2 + 1/8