e^ 5 x d x is equal to - Vidyadip

MCQ

$\int e^{5 \log x} d x$ is equal to

A
$\frac{x^5}{5}+C$
✓
$\frac{x^6}{6}+C$
C
$5 x^4+C$
D
$6 x^5+C$

✓

Answer

Correct option: B.

$\frac{x^6}{6}+C$

$\text {Let } I=\int e^{5 \log x} d x$
$=\int e^{\log x^5} d x=\int x^5 d x $
$\left[\because e^{\log x}=x\right]$
$=\frac{x^6}{6}+C$

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