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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {(1 - {x^2})\log x\;dx = } $
  • ✓
    $\left( {x - \frac{{{x^3}}}{3}} \right)\log x - \left( {x - \frac{{{x^3}}}{9}} \right) + c$
  • B
    $\left( {x - \frac{{{x^3}}}{3}} \right)\log x + \left( {x - \frac{{{x^3}}}{9}} \right) + c$
  • C
    $\left( {x + \frac{{{x^3}}}{3}} \right)\log x + \left( {x + \frac{{{x^3}}}{9}} \right) + c$
  • D
    None of these
✓

Answer

Correct option: A.
$\left( {x - \frac{{{x^3}}}{3}} \right)\log x - \left( {x - \frac{{{x^3}}}{9}} \right) + c$
a
(a)$\int_{}^{} {(1 - {x^2})\log x\,dx} = \int_{}^{} {\log x\,dx} - \int_{}^{} {{x^2}\log x\,dx} $
$ = x(\log x - 1) - \frac{{{x^3}\log x}}{3} + \frac{{{x^3}}}{9} + c$
$ = \left( {x - \frac{{{x^3}}}{3}} \right)\log x - \left( {x - \frac{{{x^3}}}{9}} \right) + c.$

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