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Indefinite Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIndefinite Integrals2 Marks
Question
Evaluate the following integrals:
$\int\frac{1}{1+\cos2\text{x}}\text{dx}$
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Answer

$\int\frac{1}{1+\cos(2\text{x})}\text{dx}$ $\Big[\therefore\ 1+\cos\theta=2\cos^2\Big(\frac{\theta}{2}\Big)\Big]$
$=\int\frac{\text{dx}}{2\cos^2\text{x}}$
$=\frac{1}{2}\int\sec^2\text{x dx}$
$=\frac{1}{2}\tan\text{x}+\text{C}$

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