# Thread: Negative Exponent Trigonometric Integrals

1. ## 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!

2. $\displaystyle \frac{1}{{\sin ^2 (x)}} = \csc ^2 (x)\,\& \,\frac{1}{{\cos ^2 (x)}} = \sec ^2 (x)$

3. 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!

4. 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!
Look here on the third page...it will help you with all sorts of trigonometric integrals

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