Q113 / 160 · AP EAMCET 2025 (24 MAY SHIFT 1) · Mathematics

For $0 < x < 1, \int\left[\operatorname{Tan}^{-1}\left(1-x+x^2\right)+\operatorname{Tan}^{-1}(1-x)\right] d x=$

  • Correct answer
    A
    $x \operatorname{Cot}^{-1} x+\log \sqrt{1+x^2}+c$
  • B
    $\mathrm{x} \operatorname{Tan}^{-1} \mathrm{x}-\log \left(1+\mathrm{x}^2\right)+\mathrm{c}$
  • C
    $x \operatorname{Cot}^{-1} x+\frac{3}{4} \log \left(1+x^2\right)+c$
  • D
    $x \operatorname{Tan}^{-1} x-\frac{3}{4} \log \sqrt{1+x^2}+c$

Hence, the correct answer is option: 'A'.

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