Evaluate the following integrals:

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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