Question

Evaluate x+9)}" alt="x^{2} \sqrt{(x^3+9)}" align="absmiddle" class="latex-formula">with subsititution using u=x^3+9

Answer 1

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

$\displaystyle\int x^2\sqrt{x^3+9}\,\mathrm dx$

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

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