JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1

\int \,\,\frac{{2{x^2} + \,\,3}}{{\left( {{x^2} - 1} \right)\,\,\left( {{x^2} + 4} \right)}}\,\,dx = a\,\,\log \,\,\left( {\frac{{x - 1}}{{x + 1}}} \right)\,\, + \,\,b\,\,{\tan ^{ - 1}}\,\,\left( {\frac{x}{2}} \right) + c

, then the value of

a

and

b

are

View answer and explanation

Correct option: D

\left( {\frac{1}{2},\,\,\frac{1}{2}} \right)

Option D

\left( {\frac{{1}}{{2}},\,\,\frac{{1}}{{2}}} \right)

is correct because by partial fraction decomposition and integration, we find that

a = \frac{1}{2}

and

b = \frac{1}{2}

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