Integral 3x + 5 / 5 akar dari (3x pangkat2 + 10x) pangkat 3

gini [tex] \int\limits { \frac{3x+5}{ \sqrt[5]{(3x^2+10x)^3} } } \, dx [/tex] bukan maksudnya bentuknya ...?


[tex] \int\limits { \frac{3x+5}{ \sqrt[5]{(3x^2+10x)^3} } } \, dx ~~~~~~~~~;~~u=3x^2+10x \\ \\ \frac{du}{dx}=6x+10 \\ \\ dx= \frac{du}{6x+10} \\ \\ \int\limits { \frac{3x+5}{ \sqrt[5]{u^3} } } \, \frac{du}{6x+10}\\ \\ = \int\limits { \frac{1}{ \sqrt[5]{u^3} } } \, \frac{du}{2}\\ \\ = \frac{1}{2}\int{u^{ \frac{3}{5} }} \,du\\ \\ =\frac{1}{2} \frac{u^{ \frac{8}{5} }}{\frac{8}{5} } +c\\ \\ = \frac{1}{2} \frac{5}{8} \sqrt[5]{u^8} +c\\ \\ = \frac{5}{16} \sqrt[5]{(3x^2+10x)^8} +c[/tex]