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STD 12 - 7.1 inderfinite integral — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 7.1 inderfinite integral4 Marks
MCQ
$\int_{}^{} {{{\tan }^{ - 1}}x\,dx = } $
  • A
    $x{\tan ^{ - 1}}x + \frac{1}{2}\log (1 + {x^2})$
  • ✓
    $x{\tan ^{ - 1}}x - \frac{1}{2}\log (1 + {x^2})$
  • C
    $(x - 1){\tan ^{ - 1}}x$
  • D
    $x{\tan ^{ - 1}}x - \log (1 + {x^2})$
✓

Answer

Correct option: B.
$x{\tan ^{ - 1}}x - \frac{1}{2}\log (1 + {x^2})$
b
(b)$\int_{}^{} {{{\tan }^{ - 1}}x\,dx} = x{\tan ^{ - 1}}x - \int_{}^{} {\frac{x}{{1 + {x^2}}}\,dx + c} $
$ = x{\tan ^{ - 1}}x - \frac{1}{2}\log (1 + {x^2}) + c.$
Note : Students should remember this question as a formula.

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