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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {x{{\tan }^{ - 1}}} xdx = $
  • ✓
    $\frac{1}{2}({x^2} + 1){\tan ^{ - 1}}x - \frac{1}{2}x + c$
  • B
    $\frac{1}{2}({x^2} - 1){\tan ^{ - 1}}x - \frac{1}{2}x + c$
  • C
    $\frac{1}{2}({x^2} + 1){\tan ^{ - 1}}x + \frac{1}{2}x + c$
  • D
    $\frac{1}{2}({x^2} + 1){\tan ^{ - 1}}x - x + c$
✓

Answer

Correct option: A.
$\frac{1}{2}({x^2} + 1){\tan ^{ - 1}}x - \frac{1}{2}x + c$
a
(a)$\int_{}^{} {x\,.\,{{\tan }^{ - 1}}x\,dx = \frac{{{x^2}}}{2}{{\tan }^{ - 1}}x - \frac{1}{2}\int_{}^{} {\frac{{{x^2} + 1 - 1}}{{1 + {x^2}}}\,dx} } $
$ = \frac{{{x^2}}}{2}{\tan ^{ - 1}}x - \frac{1}{2}x + \frac{1}{2}{\tan ^{ - 1}}x + c$
$ = \frac{1}{2}{\tan ^{ - 1}}x\,.\,({x^2} + 1) - \frac{1}{2}x + c$.

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