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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{{{{(1 + \log x)}^2}}}{x}} \;dx = $
  • A
    ${(1 + \log x)^3} + c$
  • B
    $3{(1 + \log x)^3} + c$
  • ✓
    $\frac{1}{3}{(1 + \log x)^3} + c$
  • D
    None of these
✓

Answer

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

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