# Need help on integral question

Hello, i have a question. This is integral question, but i dont have any program to write the equation with:

integral (sin5x)^(-2) dx= ?

Thank you..

## Answers and Replies

cristo
Staff Emeritus
Science Advisor
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)

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)
yes i have done using substitution method but can't solve the problem. Can you step by step show me how please? thx

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

It's your homework, not mine! Show how you did the first substitution, and we'll go from there.
ok sorry
if i substitute with sin5x,

integral (sin5x)^(-2) d(sin5x)/5cos5x

this is how far i can get if i substitute with sin5x as i cant eliminate the cos5x.
I already tried substituting with cosec5x and sec5x, but still no solution.

jakcn001
With -d[cot(x)]=(sinx)^(-2) dx ,you can solve it easily.Have a try!

cristo
Staff Emeritus
Science Advisor
ok sorry
if i substitute with sin5x,

integral (sin5x)^(-2) d(sin5x)/5cos5x

this is how far i can get if i substitute with sin5x as i cant eliminate the cos5x.
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 $$5 \int \frac{du}{u^2\sqrt{1-u^2}}$$.

There you go, I've done one step for you. Now, try the substitution v=1/u.
I already tried substituting with cosec5x and sec5x, but still no solution.
If you look back, I said you'll need a few substitutions!

With -d[cot(x)]=(sinx)^(-2) dx ,you can solve it easily.Have a try!
I did allude to that in my first post.

ok thx guys i understand now