Evaluate the following integrals:

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 $t=\tan x$

$\Rightarrow \frac{2 \tan ^{\frac{5}{2}} x}{5}+c$

Leave a comment

None
Free Study Material