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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{1}{{x{{\cos }^2}(1 + \log x)}}\;dx = } $
  • ✓
    $\tan \,(1 + \log x) + c$
  • B
    $\cot \,(1 + \log x) + c$
  • C
    $ - \tan \,(1 + \log x) + c$
  • D
    $ - \cot (\,1 + \log x) + c$
✓

Answer

Correct option: A.
$\tan \,(1 + \log x) + c$
a
(a) Put $1 + \log x = t \Rightarrow \frac{1}{x}\,dx = dt,$ then
$\int_{}^{} {\frac{1}{{x{{\cos }^2}(1 + \log x)}}\,dx} = \int_{}^{} {\frac{{dt}}{{{{\cos }^2}t}} = \int_{}^{} {{{\sec }^2}t\,dt} } $
$ = \tan t + c = \tan (1 + \log x) + c.$

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