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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 + 1)dx = } $
  • ✓
    $(x + 1)\log (x + 1) - x + c$
  • B
    $(x + 1)\log (x + 1) + x + c$
  • C
    $(x - 1)\log (x + 1) - x + c$
  • D
    $(x - 1)\log (x + 1) + x + c$
✓

Answer

Correct option: A.
$(x + 1)\log (x + 1) - x + c$
a
(a)$\int_{}^{} {\log (x + 1)\,dx} = x\log (x + 1) - \int_{}^{} {\frac{x}{{x + 1}}\,dx + c} $
$ = x\log (x + 1) - x + \log (x + 1) + c = (x + 1)\log (x + 1) - x + c$.

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