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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1
∫  x3−  1x3+  x  dx\int \,\,\frac{{{x^3} - \,\,1}}{{{x^3} + \,\,x}}\,\,dx is equal to
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Correct option: B
x  −  log⁡  x  +  12  log⁡  (x2+1)−  tan⁡−1  x+  Cx\,\, - \,\,\log \,\,x\,\, + \,\,\frac{1}{2}\,\,\log \,\,\left( {{x^2} + 1} \right) - \,\,{\tan ^{ - 1}}\,\,x + \,\,C
Option B is correct because after performing polynomial long division and partial fraction decomposition, the integral evaluates to x−log⁡x+12log⁡(x2+1)−tan⁡−1x+Cx - \log x + \frac{1}{2}\log(x^2 + 1) - \tan^{-1}x + C.

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