Question

integral 4x^2 * raiz (8x^3+5)dx

Answer 1

$\int\limits( {4x^2 \sqrt{8x^3+5} )} \, dx \\ \\ \\ u=8x^3+5 \ \ \ \ \ \ \ \ \ \ \ \ \ \ du= 24x^2dx \\ \\ dx= \frac{1}{24x^2}du \\ \\ \\ \int\limits( {4x^2 \sqrt{u} )} \, \frac{1}{24x^2}du$


$\int\limits( {\not4x^2 u^{ \frac{1}{2} } )} \, \frac{1}{\not24x^2}du$

$\frac{1}{6} \int\limits u^{ \frac{1}{2} } \, du \\ \\ \\ \frac{1}{6} * \frac{u^{ \frac{3}{2}} }{\frac{3}{2}}$

$\frac{1}{6} *\frac{2}{3}} {u^{ \frac{3}{2}}+C$

$\frac{1}{9} {u^{ \frac{3}{2}}+C$

$\int\limits( {4x^2 \sqrt{8x^3+5} )} \, dx=\boxed{\boxed{\frac{1}{9} {(8x^3+5)^{ \frac{3}{2}}+C}}}$