JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \frac{d x}{\left(x^2+1\right)\left(x^2+4\right)}=P \tan ^{-1} x+Q \tan ^{-1} \frac{x}{2}+c

, then

P+Q=

View answer and explanation

Correct option: D

P+Q=\frac{1}{6}

Option D,

P+Q=\frac{{1}}{{6}}

, is correct because partial fraction decomposition and integration yield

P = \frac{{1}}{{3}}

and

Q = -\frac{{1}}{{6}}

, so their sum is

\frac{{1}}{{6}}

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