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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}{{\sec }^2}(\log x)dx = } $
  • ✓
    $\tan (\log x) + c$
  • B
    $\log (\sec x) + c$
  • C
    $\log (\tan x) + c$
  • D
    $\sec (\log x)\;.\;\tan (\log x) + c$
✓

Answer

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

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