Question

Find the Integration of $e^{3lo{g}_{e}x}$ with respect to x.

Answer 1

We are given $I=\int e^{3log{e}^x}dx$

here $e^{3log{e}^x}=e^{\log e^{x^3}=x^3}$

(From the logarithmic properties )

So, $I=\int x^{3}dx$

$=\frac{x^4}{4}+c.$

$I=\frac{1}{4}{e}^{\log e^{x^4}+c.}$

$I=\frac{1}{4}{e}^{4\log e^x}+c$