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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {x\log xdx = } $
  • A
    $\frac{{{x^2}}}{2}\log x - \frac{{{x^2}}}{2} + c$
  • ✓
    $\frac{{{x^2}}}{2}\log x - \frac{{{x^2}}}{4} + c$
  • C
    $\frac{{{x^2}}}{2}\log x + \frac{{{x^2}}}{2} + c$
  • D
    None of these
✓

Answer

Correct option: B.
$\frac{{{x^2}}}{2}\log x - \frac{{{x^2}}}{4} + c$
b
(b)$\int_{}^{} {x\log x\,dx} = \frac{{{x^2}}}{2}\log x - \int_{}^{} {\frac{1}{x}.\frac{{{x^2}}}{2}dx + c} = \frac{{{x^2}\log x}}{2} - \frac{{{x^2}}}{4} + c$.

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