[tex] \int\limits { \frac{3x^{2} }{ \sqrt[3]{2 x^{3} + 7 } } } \, dx [/tex]

[tex] \int\limits { \frac{3x^{2} }{ \sqrt[3]{2 x^{3} + 7 } } } \, dx~~~~~~~~;~~u=2x^3 \\ \\ \frac{du}{dx}=6x^2 \\ \\ dx= \frac{du}{6x^2} \\ \\ \\ \int\limits { \frac{3x^{2} }{ \sqrt[3]{u + 7 } } } \, \frac{du}{6x^2} \\ \\ =\int\limits { \frac{1}{ 2\sqrt[3]{u + 7 } } } \, du \\ \\ =\frac{1}{2} \int\limits { (u+7)^ {-\frac{1}{3}} } \, du \\ \\ =\frac{1}{2} \frac{(u+7)^ {\frac{2}{3}} }{\frac{2}{3}} \\ \\ = \frac{3}{4} \sqrt[3]{(u+7)^2} \\ \\ = \frac{3}{4} \sqrt[3]{(2x^3+7)^2} [/tex]