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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^x}(1 + \log x)\,\,dx} $ is equal to
  • ✓
    ${x^x}$
  • B
    ${x^{2x}}$
  • C
    ${x^x}\log x$
  • D
    $\frac{1}{2}{(1 + \log x)^2}$
✓

Answer

Correct option: A.
${x^x}$
a
(a) $I = \int {{x^x}(1 + \log x)\,dx} $.
Put ${x^x} = t$, then ${x^x}(1 + \log x)dx = dt$
$\therefore I = \int {dt} $ $ \Rightarrow I = t + C$ $ \Rightarrow I = {x^x} + C$.

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