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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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∫  2x2  +  3(x2−1)  (x2+4)  dx=a  log⁡  (x+1x−1)  +  b  tan⁡−1  x2\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}}\,\,\frac{x}{2}, then (a,   b)\left( {a,\,\;b} \right) is

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Correct option: A
(−1/2,    1/2)\left( { - 1/2,\;\,\,1/2} \right)
Option A ((-1/2, 1/2)) is correct because by performing partial fraction decomposition and integrating, we find the coefficients a and b to be -1/2 and 1/2, respectively.

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