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Integrals — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSIntegrals1 Mark
Question
Integrate the function $x \sec^2 x$
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Answer

Let I $= x \sec^{2 }x$
Now, integrating by parts, we get,
$I=x \int \sec ^{2} x d x-\int\left\{\left(\frac{d}{d x} x\right) \int \sec ^{2} x d x\right\} d x$ 
$= x \tan x-\int (1) (\tan x) d x$ 
$= x \tan x+\log |\cos x|+c$ 

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