Evaluate: ( 2 ^2x- 2x ^2x )dx - Vidyadip

Question

Evaluate:
$\int\Big(\frac{2\cos^2\text{x}-\cos2\text{x}}{\cos^2\text{x}}\Big)\text{dx}$

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Answer

$\int\Big(\frac{2\cos^2\text{x}-\cos2\text{x}}{\cos^2\text{x}}\Big)\text{dx}$
$=\int\Big(\frac{2\cos^2\text{x}-(2\cos^2\text{x}-1)}{\cos^2\text{x}}\Big)\text{dx}$ $[\because\cos2\text{x}=2\cos^2\text{x}-1]$
$=\int\text{sec}^2\text{x}\text{ dx}$
$=\tan\text{x}+\text{c}$

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