Matematica 2 Ing. IndustrialClase: 4192

Tema: Formas de integracion

1. du = u+ C

2. undu =un+1

n+ 1+ C, n 6= 1

3.1udu = ln |u|+ C

4. eudu = eu + C

5 audu =au

ln a+ C

6. senu du = cosu+ C7. cosu du = senu+ C

8. tanu du = ln |cosu|+ C9 cotu = ln |senu|+ C10. secu du = ln |secu+ tanu|+ C11. cscu du = ln |cscu cotu|+ C12. sec2 u = tanu+ C

13. csc2 u = cotu+ C14. secu tanu = secu+ C15. cscu cotu = cscu+ C

161

u2 + a2du =

1aarctan

(ua

)+ C

17.1

a2 u2 du = arcsen(ua

)+ C

Ejemplos. Calcular

1.(x4 + 4x3 1

x5

)dx

2. x 3(x2 + 3)2dx

3.(3 x3)4 x2dx

4. x2 tan(3 x3) dx

1