use u=cosx and then do another trig substitution if you get stuck.
Without a trigonometric substitution, doing in this way yields a very nice answer:
[LaTeX ERROR: Convert failed] " alt=" \displaystyle = \int\frac{u^2}{(u+1)(u-1)}\;{du} = \int \left\{\frac{1}{2(u-1)}-\frac{1}{2(u+1)}+1 \right\}\;{du}[/Math] [LaTeX ERROR: Convert failed] " />[LaTeX ERROR: Convert failed]
Hint: [LaTeX ERROR: Convert failed] .I get to the integral of 1/(sinxcos²x)
What would I do next