Need help on integral question

This is one of those you should really know, since it can be rewritten cosec²(5x).

However, if you don't know the antiderivative, then it can be worked out by a few substitutions, the first being u=sin(5x)

 

It's your homework, not mine! Show how you did the first substitution, and we'll go from there.

 

With -d[cot(x)]=(sinx)^(-2) dx ,you can solve it easily.Have a try!

 

If you've substituted, why do you still have functions of x in the integral? If you let u=sin(5x), then du=5cos(5x)dx=5[sqrt(1-u²)]. This transforms your integral to [tex]5 \int \frac{du}{u^2\sqrt{1-u^2}}[/tex].

There you go, I've done one step for you. Now, try the substitution v=1/u.

If you look back, I said you'll need a few substitutions!

I did allude to that in my first post.