# Need help on integral question

1. Mar 19, 2007

### Mag|cK

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..

2. Mar 19, 2007

### cristo

Staff Emeritus
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)

3. Mar 19, 2007

### Mag|cK

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

4. Mar 19, 2007

### cristo

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

5. Mar 19, 2007

### Mag|cK

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.

6. Mar 19, 2007

### jakcn001

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

7. Mar 19, 2007

### cristo

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

I did allude to that in my first post.

8. Mar 20, 2007

### Mag|cK

ok thx guys i understand now