Lösung 2.2:1c
Aus Online Mathematik Brückenkurs 2
With the given variable substitution, \displaystyle u=x^{3} we obtain
\displaystyle du=\left( x^{3} \right)^{\prime }\,dx=3x^{2}\,dx
and because the integral contains
\displaystyle x^{2}
as a factor, we can bundle it together with
\displaystyle dx
and replace the combination with
\displaystyle \frac{1}{3}\,du,
\displaystyle \int{e^{x^{3}}x^{2}\,dx=\left\{ u=x^{3} \right\}}=\int{e^{u}}\frac{1}{3}\,du=\frac{1}{3}e^{u}+C
Thus, the answer is
\displaystyle \int{e^{x^{3}}x^{2}\,dx=}\frac{1}{3}e^{x^{3}}+C
where
\displaystyle C
is an arbitrary constant.
