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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_{}^{} {\frac{{2x{{\tan }^{ - 1}}{x^2}}}{{1 + {x^4}}}} \;dx = $
  • A
    ${[{\tan ^{ - 1}}{x^2}]^2} + c$
  • ✓
    $\frac{1}{2}{[{\tan ^{ - 1}}{x^2}]^2} + c$
  • C
    $2{[{\tan ^{ - 1}}{x^2}]^2} + c$
  • D
    None of these
✓

Answer

Correct option: B.
$\frac{1}{2}{[{\tan ^{ - 1}}{x^2}]^2} + c$
b
(b) Put $t = {\tan ^{ - 1}}{x^2} \Rightarrow dt = \frac{1}{{1 + {x^4}}}\,2x\,dx,$ then
$\int_{}^{} {\frac{{2x{{\tan }^{ - 1}}{x^2}}}{{1 + {x^4}}}} \,dx = \int_{}^{} {t\,dt} = \frac{{{t^2}}}{2} + c = \frac{1}{2}{({\tan ^{ - 1}}{x^2})^2} + c.$

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