Question

Evaluate x
`x^(2) √((x^3+9))`with subsititution using u=x^3+9

Answer 1

It sounds like you're talking about an integral, namely

`\displaystyle\int x^2√(x^3+9)\,\mathrm dx`

Substitute u = x ³ + 9, so that du = 3x ² dx. Then

`\displaystyle\int x^2√(x^3+9)\,\mathrm dx=\frac13\int√(u)\,\mathrm du=\frac13*\frac23u^(\frac32)+C=\boxed{\frac29(x^3+9)^(\frac32)+C}`