Question

What is the integral of x^2 e^(2x^3 +4) dx

Answer 1

`\displaystyle\int x^2e^(2x^3+4)\,\mathrm dx`

Let
`y=2x^3+4`, then
`\mathrm dy=6x^2\,\mathrm dx`. So


`\displaystyle\int x^2e^(2x^3+4)\,\mathrm dx=\frac16\int e^y\,\mathrm dy=\frac16e^y+C`

Back-substitute to get this in terms of
`x`:


`\frac16e^(2x^3+4)+C`