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Definite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
$\int_1^{ e } \frac{ e ^x}{x}(1+x \log x) d x=$
  • ✓
    $e^e$
  • B
    $e^e-e$
  • C
    $e ^{ e }+ e$
  • D
    $e^e+\frac{e}{2}$
✓

Answer

Correct option: A.
$e^e$
(A)
$\int_1^{ e } \frac{ e ^x}{x}(1+x \log x) d x=\int_1^{ e } e ^x\left(\frac{1}{x}+\log x\right) d x$
$=\left[ e ^x \cdot \log x\right]_1^{ e }= e ^{ e }$

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