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

$\text{The given integral is,}$
$\int x^2{10}^{x^3}dx$
$\text{Using substitution method of integration, on substituting }{x}^3\text{ with t}$
$x^3=t$
$3x^{2}dx=dt$
$x^{2}dx=\frac{dt}{3}$
$\text{Then the transformed integral we get is,}$
$I=\int \frac{{10}^t}{3}dt$
$=\frac{1}{3}\int {10}^{t}dt$
$\text{Using exponential rule, }\int a^{x}dx=\frac{a^x}{\ln (a)}+C$
$I=\frac{1}{3}\int {10}^{t}dt$
$=\frac{1}{3}[\frac{{10}^t}{\ln (10)}]+C$
$\text{On puttinf back the value of t, we get}$
$I=\frac{{10}^{x^3}}{3\ln (10)}+C$
$\text{Therefore, the value of the given integral is }\frac{{10}^{x^3}}{3\ln (10)}+C$