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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1
∫  x  dxx2  +  4x  +  5\int \,\,\frac{{x\,\,dx}}{{{x^2}\,\, + \,\,4x\,\, + \,\,5}} is equal to
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Correct option: D
12  log⁡  (x2  +  4x  +  5)  −  2  tan⁡−1  (x+2)+c\frac{1}{2}\,\,\log \,\,\left( {{x^2}\,\, + \,\,4x\,\, + \,\,5} \right)\,\, - \,\,2\,\,{\tan ^{ - 1}}\,\,\left( {x + 2} \right) + c
Option B (12  log⁡  (x2 + 4x + 5) − tan⁡−1  (x+2)+c\frac{1}{2}\,\,\log \,\,\left( {{x^2}\, + \,4x\, + \,5} \right)\, - \,{\tan ^{ - 1}}\,\,\left( {x + 2} \right) + c) is correct. Completing the square and splitting the integral leads to the correct result.

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