[tex]\displaystyle\int x^2e^{2x^3+4}\,\mathrm dx[/tex]
Let [tex]y=2x^3+4[/tex], then [tex]\mathrm dy=6x^2\,\mathrm dx[/tex]. So
[tex]\displaystyle\int x^2e^{2x^3+4}\,\mathrm dx=\frac16\int e^y\,\mathrm dy=\frac16e^y+C[/tex]
Back-substitute to get this in terms of [tex]x[/tex]:
[tex]\dfrac16e^{2x^3+4}+C[/tex]
