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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {\frac{1}{{x\sqrt {1 + \log x} }}\;dx = } $
  • A
    $\frac{2}{3}{(1 + \log x)^{3/2}} + c$
  • B
    ${(1 + \log x)^{3/2}} + c$
  • ✓
    $2\sqrt {1 + \log x} + c$
  • D
    $\sqrt {1 + \log x} + c$
✓

Answer

Correct option: C.
$2\sqrt {1 + \log x} + c$
c
(c)Put $t = 1 + \log x \Rightarrow dt = \frac{1}{x}dx$, then
$\int_{}^{} {\frac{{dx}}{{x\sqrt {1 + \log x} }}} = \int_{}^{} {\frac{{dt}}{{{t^{1/2}}}} = 2{t^{1/2}} + c} = 2{(1 + \log x)^{1/2}} + c$.

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