# Negative Exponent Trigonometric Integrals

• Apr 23rd 2008, 08:04 AM
Doky53
Negative Exponent Trigonometric Integrals
I've run into a couple of integrals I didn't know how to solve. I managed to find the solution to only one of them (INTEGRAL 1/sin x = - ln |csc x + cot x| + C)

I'd like help with the following, (kind of urgent - doing some tutoring and need to clear up stuff like this in case it comes up):

1. INTEGRAL 1/sin
^2 (x)
2. INTEGRAL 1/cos^2 (x)

I'm guessing the solutions for both are similar..and I'm assuming there may be a formula for integrals such as sin^- n (x) (or cos), but I'm mostly interested in the exponent - 2.

Thanks in advance to anyone who gives it a shot!
• Apr 23rd 2008, 08:11 AM
Plato
$\frac{1}{{\sin ^2 (x)}} = \csc ^2 (x)\,\& \,\frac{1}{{\cos ^2 (x)}} = \sec ^2 (x)
$
• Apr 23rd 2008, 08:17 AM
Doky53
Yeah, I can figure as much... but it's the SOLVING part that I'm not sure of. Obviously, 1/sin x = csc x, so if I know the integral of one, I know the other... I guess I could have reformulated my question to read INTEGRAL csc^2 (x) and INTEGRAL sec^2 (x)..but the solving of those integrals is what I need help with. Links to solutions or solutions themselves are fine.

Thanks for helping! (Clapping)
• Apr 23rd 2008, 08:58 AM
Mathstud28
Quote:

Originally Posted by Doky53
Yeah, I can figure as much... but it's the SOLVING part that I'm not sure of. Obviously, 1/sin x = csc x, so if I know the integral of one, I know the other... I guess I could have reformulated my question to read INTEGRAL csc^2 (x) and INTEGRAL sec^2 (x)..but the solving of those integrals is what I need help with. Links to solutions or solutions themselves are fine.

Thanks for helping! (Clapping)

Look here on the third page...it will help you with all sorts of trigonometric integrals

http://www.mathhelpforum.com/math-he...-tutorial.html