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STD 12 - 7.1 inderfinite integral — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {\frac{{dx}}{{2\sqrt x (1 + x)}} = } $
  • A
    $\frac{1}{2}{\tan ^{ - 1}}(\sqrt x ) + c$
  • ✓
    ${\tan ^{ - 1}}(\sqrt x ) + c$
  • C
    $2{\tan ^{ - 1}}(\sqrt x ) + c$
  • D
    None of these
✓

Answer

Correct option: B.
${\tan ^{ - 1}}(\sqrt x ) + c$
b
(b) $I = \int {\frac{{dx}}{{2\sqrt x (1 + x)}}} $

Put $\sqrt x \, = t$==> $\frac{1}{{2\sqrt x }}dx = dt$

$\therefore I = \int {\frac{{dt}}{{1 + {t^2}}}} = {\tan ^{ - 1}}t + c$$ = {\tan ^{ - 1}}(\sqrt x ) + c$.

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