Question

How do you use substitution to integrate `6 x e^{4 x^2} dx`?

Answer 1

`3/4e^(4x^2)+C`

Explanation:

Let `t=4x^2`, then `dt=8xdx => xdx=dt/8`. So,
`int6xe^(4x^2)dx=int6dt/8 e^t=3/4inte^tdt=3/4e^t+C=3/4e^(4x^2)+C`