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CBSE Class 12 · 2011 · Indefinite IntegralsVery Short Answer

Write the value of

\int \frac{2 - 3 s i n x}{c o s ^{2} x} d x

Answer: $2 tan x - 3 sec x + C$

Solution

Split the integrand into standard pieces:

\frac{2 - 3 sin x}{cos ^{2} x} = 2 sec^{2} x - 3 \frac{sin x}{cos ^{2} x} .

Now

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

, and for the second piece put

z = cos x

so

\int \frac{sin x}{cos ^{2} x} d x = \frac{1}{cos x} = sec x

. Hence

2 tan x - 3 sec x + C

CBSE Class 12 Board · 2011 · Subjective

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