Pregunta: If ∫243x2x3-12dx=∫abu2du, then:

Since $3$ is constant with respect to $\mathrm{x}$ , move $3$ out of the integral.

$3{\int }_2^4{\mathrm{x}}^2\sqrt{{\mathrm{x}}^3-1}\mathrm{d}\mathrm{x}$

Let $\mathrm{u}={\mathrm{x}}^3-1$ . Then $\mathrm{d}\mathrm{u}=3{\mathrm{x}}^2\mathrm{d}\mathrm{x}$ , so $\frac{1}{3}\mathrm{d}\mathrm{u}={\mathrm{x}}^2\mathrm{d}\mathrm{x}$ . Rewrite using $\mathrm{u}$ ...