I have a step in my book that I cannot figure $\displaystyle \int cot^2\theta csc^2 \theta d \theta$
and next step is $\displaystyle -\frac{1}{3}cot^3\theta +c$
I used $\displaystyle 1+cot^2\theta = csc^2 \theta$ but that does not work -
I have a step in my book that I cannot figure $\displaystyle \int cot^2\theta csc^2 \theta d \theta$
and next step is $\displaystyle -\frac{1}{3}cot^3\theta +c$
I used $\displaystyle 1+cot^2\theta = csc^2 \theta$ but that does not work -
suppose $\displaystyle t = cot \theta$
so, $\displaystyle dt=-csc^2 \theta \Rightarrow -dt=csc^2 \theta$
now, $\displaystyle \int cot^2\theta csc^2 \theta d \theta$
$\displaystyle = -\int t^2 dt$
$\displaystyle =-\frac{t^3}{3} +c$
$\displaystyle =-\frac{1}{3}cot^3\theta +c$