# How do you find the integral of #f(x)=1/(1-sinx)# using integration by parts?

##### 1 Answer

Apr 10, 2018

#### Explanation:

#intdx/(1-sinx)#

Let's first get this into a more workable form by multiplying through by the conjugate:

#=int1/(1-sinx)*(1+sinx)/(1+sinx)dx#

#=int(1+sinx)/(1-sin^2x)dx#

Recall that

#=int(1+sinx)/cos^2xdx#

Splitting up the integral by addition:

#=int1/cos^2xdx+intsinx/cos^2xdx#

Rewrite using the identities

#=intsec^2xdx+intsecxtanxdx#

And then, from the knowledge that

#=tanx+secx+C#

No integration by parts required!