Question:
Evaluate the following integrals:
$\int \frac{\sec ^{2} x}{\tan x+2} d x$
Solution:
Assume $\tan x+2=t$
$d(\tan x+2)=d t$
$\left(\sec ^{2} x d x\right)=d t$
Put $\mathrm{t}$ and $\mathrm{dt}$ in given equation we get
$\Rightarrow \int \frac{\mathrm{d} t}{\mathrm{t}}$
$=\ln |\mathrm{t}|+\mathrm{c}$
But $t=\tan x+2$
$=\ln |\tan x+2|+c$
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