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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
If $\int_{}^{} {\ln ({x^2} + x)dx = x\ln ({x^2} + x) + A} $, then $A = $
  • A
    $2x + \ln (x + 1) + $constant
  • B
    $2x - \ln (x + 1) + $constant
  • C
    Constant
  • ✓
    None of these
✓

Answer

Correct option: D.
None of these
d
(d)$\int_{}^{} {\log ({x^2} + x)\,dx} = \int_{}^{} {\log x\,dx} + \int_{}^{} {\log (x + 1)\,dx} $
$ = x\log x - x + x\log (x + 1) - x + \log (x + 1)$
$ = x\left\{ {(\log x + \log (x + 1)} \right\} - 2x + \log (x + 1)$
$ = x\log ({x^2} + x) - 2x + \log (x + 1)$
Equating it to the given integration, we get
$A = - 2x + \log (x + 1)$.

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