\int {2x + 3}/{x^{3} + x^{2}−2x}dx = ?

Correct Answer is : 53log⁡|.x−1|.−32log⁡|.x|.−16log⁡|.x+2|.+c

\frac{5}{3}\log ⁡|.x−1|. + \frac{3}{2}\log ⁡|.x|. + \frac{1}{6}\log ⁡|.x + 2|. + c

\frac{5}{3}\log ⁡|.x−1|.−\frac{3}{2}\log ⁡|.x|.−\frac{1}{6}\log ⁡|.x + 2|. + c

\frac{5}{3}\log ⁡|.x−1|. + \frac{3}{2}\log ⁡|.x|.−\frac{1}{6}\log ⁡|.x + 2|. + c

\frac{5}{3}\log ⁡|.x−1|.−\frac{3}{2}\log ⁡|.x|. + \frac{1}{6}\log ⁡|.x−2|. + c

AAI ATC Junior Executive 21 Feb 2023 Shift 1 Paper

Question : 119 of 120

Marks: +1, -0

∫ \;{2x + 3}/{x^{3} + x^{2}−2x}dx = ?

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