# Math Help - Trouble with integrating secxcosecx

1. ## Trouble with integrating secxcosecx

Hi there,

I'm trying to evaluate how the strength of a composite varies through a given range of orientation and in order to do this I need to integrate secxcosex and then evaluate the integral through a small range of x (depending on the composite the upper bound is typically around 0.1 to 0.2 rads and the lower bound is typically between 0.01 and 0.02 rads).

However, I'm stuck on how to go about integrating secxcosecx. I tried integrating by parts but got stuck. I took u as equal to secx and dv as equal to cosecx. The first part of the integral (the 'uv' term) seemed to be fine (got secxln(cosecx+cotx)) but the next part that I need to integrate looks like a nightmare!:

ln(cosecx+cotx)*(secxtanx)

Anyone got any suggestions?

Thanks.

2. Originally Posted by compositesguy
Hi there,

I'm trying to evaluate how the strength of a composite varies through a given range of orientation and in order to do this I need to integrate secxcosex and then evaluate the integral through a small range of x (depending on the composite the upper bound is typically around 0.1 to 0.2 rads and the lower bound is typically between 0.01 and 0.02 rads).

However, I'm stuck on how to go about integrating secxcosecx. I tried integrating by parts but got stuck. I took u as equal to secx and dv as equal to cosecx. The first part of the integral (the 'uv' term) seemed to be fine (got secxln(cosecx+cotx)) but the next part that I need to integrate looks like a nightmare!:

ln(cosecx+cotx)*(secxtanx)

Anyone got any suggestions?

Thanks.
$\int \sec x \csc x \,dx = \int \frac{1}{\sin x \cos x} dx = \int \frac{\sec^2 x}{\tan x} dx$

then let $u = \tan x$

3. Excellent! Thanks for the help!

Showing me to how to rearrange to an integral of the form f'x/fx made this much simpler!