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Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
MCQ
$\int e^x\left(\frac{x \log x+1}{x}\right) d x$ is equal to
  • A
    $\log \left(e^x \log x\right)+c$
  • B
    $\frac{e^x}{x}+c$
  • C
    $x \log x+e^x+c$
  • ✓
    $e^x \log x+c$
✓

Answer

Correct option: D.
$e^x \log x+c$
$\text {Let } I=\int e^x\left(\log x+\frac{1}{x}\right) d x$
$\Rightarrow I=e^x \log x+c $
$\left(\because \int e^x\left[f(x)+f^{\prime}(x)\right] d x=e^x f(x)+c\right)$

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