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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {\log x(\log x + 2)\;dx = } $
  • ✓
    $x{(\log x)^2} + c$
  • B
    $x{(1 + \log x)^2} + c$
  • C
    $x[1 + {(\log x)^2}] + c$
  • D
    None of these
✓

Answer

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

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