Prove

Question:

$\frac{\sec ^{2} x}{\sqrt{\tan ^{2} x+4}}$

Solution:

Let $\tan x=t$

$\therefore \sec ^{2} x d x=d t$

$\Rightarrow \int \frac{\sec ^{2} x}{\sqrt{\tan ^{2} x+4}} d x=\int \frac{d t}{\sqrt{t^{2}+2^{2}}}$

$=\log \left|t+\sqrt{t^{2}+4}\right|+C$

$=\log \left|\tan x+\sqrt{\tan ^{2} x+4}\right|+\mathrm{C}$

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