Question

What is `int u^3-lnu ((du)/dx)` if `u=3x`?

Answer 1

Given: `int u^3-ln|u| ((du)/dx); u = 3x` then `(du)/dx = 3`

Moving the multiplication by `(du)/dx` in front of the logarithm:

`int (u^3-3ln|u|) du = u^4/4+(3u)(ln|u|-1)+ C`

Reversing the substitution for u:

`int (u^3-3ln|u|) du = (x^3)^4/4+(3(x^3))(ln|3^3|-1)+ C`