Question:
Evaluate the following integrals:
$\int \tan ^{3 / 2} x \sec ^{2} x d x$
Solution:
Assume $\tan x=t$
$d(\tan x)=d t$
$\sec ^{2} x d x=d t$
$\therefore$ Substituting $\mathrm{t}$ and dt in given equation we get
$\Rightarrow \int t^{\frac{3}{2}} d t$
$\Rightarrow \frac{2 t^{\frac{5}{2}}}{5}+c$
But $t=\tan x$
$\Rightarrow \frac{2 \tan ^{\frac{5}{2}} x}{5}+c$
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