Интеграл (x^2+2)^2/корень из х по dx

[latex]= \frac{2}{9} * x^{9/2} +4* \frac{2}{5} * x^{5/2} +4*2* x^{1/2} = \frac{2}{9} * x^{9/2} + \frac{8}{5} * x^{5/2} + 8 * x^{1/2} = [/latex][latex] \int { \frac{ (x^{2}+2) ^{2} }{ \sqrt{x} } \, dx = \int \frac{x^{4}+4x^{2}+4}{ \sqrt{x} } \, dx = \int { \frac{ x^{4} }{ \sqrt{x} } \, dx + \int { \frac{4 x^{2} }{ \sqrt{x} } \, dx + \int { \frac{4} \sqrt{x} } \, dx \int { x^{7/2}} \, dx +4 \int\ { x^{3/2} } \, dx +4 \int { x^{-1/2}} \, dx [/latex]