Evaluate: 2x+2 ^2x ^2x dx - Vidyadip

Question

Evaluate: $\int\frac{\cos2\text{x}+2\sin^2\text{x}}{\cos^2\text{x}}\text{dx}$

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Answer

$\int\frac{\cos2\text{x}+2\sin^2\text{x}}{\cos^2\text{x}}$
$\int\frac{2\cos^2\text{x}-1+2(1-\cos^2\text{x})}{\cos^2\text{x}}\text{dx}$
$\int\Big(2-\frac{1}{\cos^2\text{x}}+\frac{2}{\cos^2\text{x}}-1\Big)\text{dx}$
$\int\Big(1+\frac{1}{\cos^2\text{x}}\Big)\text{dx}$
$\text{x}+\int\text{sec}^2\text{x}\text{dx}$
$\text{x}+\tan\text{x}+\text{C}$

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