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CBSE Class 12 · 2018 · Indefinite IntegralsShort Answer

Evaluate

\int \frac{c o s 2 x + 2 s i n ^{2} x}{c o s ^{2} x} d x

Answer: $tan x + C$

Solution

Use

cos 2 x = 1 - 2 sin^{2} x

in the numerator:

cos 2 x + 2 sin^{2} x = (1 - 2 sin^{2} x) + 2 sin^{2} x = 1.

So the integrand is

\frac{1}{cos ^{2} x} = sec^{2} x

, and

\int sec^{2} x d x = tan x + C

CBSE Class 12 Board · 2018 · Subjective

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