# Evaluate the following integrals. int x^210^{x^3}dx

Chaya Galloway 2021-02-24 Answered
Evaluate the following integrals.
$\int {x}^{2}{10}^{{x}^{3}}dx$
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Asma Vang

$\text{The given integral is,}$
$\int {x}^{2}{10}^{{x}^{3}}dx$

${x}^{3}=t$
$3{x}^{2}dx=dt$
${x}^{2}dx=\frac{dt}{3}$
$\text{Then the transformed integral we get is,}$
$I=\int \frac{{10}^{t}}{3}dt$
$=\frac{1}{3}\int {10}^{t}dt$

$I=\frac{1}{3}\int {10}^{t}dt$
$=\frac{1}{3}\left[\frac{{10}^{t}}{\mathrm{ln}\left(10\right)}\right]+C$
$\text{On puttinf back the value of t, we get}$
$I=\frac{{10}^{{x}^{3}}}{3\mathrm{ln}\left(10\right)}+C$