Evaluate a Definite Integral Involving Trigonometric Function

[daring horizon]

Hi everyone
I feel like there's a trick or simplification, but i'm not sure how to approach it... so
any ideas or hints would be really appreciated and thanks!

[weak forum]

I think a variable change like u=cos(t) or u=tan(t/2) can help you

[crimson dagger]

I’m not sure but I think you could use u sub where u = -2xcos(t) and so du would be 2xsin(t)dx, which is basically in the numerator except you have to multiply it by 2 and 1/2 on the outside, and so the integral becomes 1/(u+x^2+1) du

Don’t take my word for it though

[gaunt blaze]

literally just set u = the entire denominator, it is with respect to t not x