Question

How do you integrate `e^7x^3 x^2 dx`?

Answer 1

`=(e^7)/6 (x^6) +C`

Explanation:

`int e^7x^3x^2 \dx`

I can see two approaches 1) combining the `x` terms or 2) doing u substitution. first lets express this differently by moving out the constant

`e^7int x^3x^2 \dx`
1)

`e^7int x^5\\dx`
`(e^7)/6 (x^6)+C`

2)
now i will use u substitution and let `u=x^3` then
`(du)/(dx) =3x^2`
`1/3du=x^2 dx`

now substituting this back in
`e^7int u1/3 \\du`
`(e^7)/3int u \\du`

`=(e^7)/3 (u^2)/2 +C`
now we place replace u
`=(e^7)/6 (x^3)^2 +C`
`=(e^7)/6 (x^6) +C`