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7.1 inderfinite integral — Maths STD 12 Science — Question

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

Answer

Correct option: C.
$\frac{1}{3}{(x + \log x)^3} + c$
c
(c) Put $t = x + \log x \Rightarrow dt = \left( {1 + \frac{1}{x}} \right)\,dx,$ then
$\int_{}^{} {\frac{{(x + 1){{(x + \log x)}^2}}}{x}\,dx} = \int_{}^{} {{t^2}dt} = \frac{{{t^3}}}{3} + c$
$ = \frac{1}{3}{(x + \log x)^3} + c.$

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