What is the integral of x/(\sqrt[3]{x+10)} ?

The integral of x/(\sqrt[3]{x+10)} is 3/5 (x+10)^{5/3}-15(x+10)^{2/3}+C

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integral of x/(\sqrt[3]{x+10)}

\frac{3}{5} (x + 10)^{\frac{5}{3}} - 15 (x + 10)^{\frac{2}{3}} + C

Solution steps

Apply u-substitution

Expand

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

\int u^{\frac{2}{3}} d u = \frac{3}{5} u^{\frac{5}{3}}

= \frac{3}{5} u^{\frac{5}{3}} - 15 u^{\frac{2}{3}}

Substitute back

u = x + 10

= \frac{3}{5} (x + 10)^{\frac{5}{3}} - 15 (x + 10)^{\frac{2}{3}}

Add a constant to the solution

= \frac{3}{5} (x + 10)^{\frac{5}{3}} - 15 (x + 10)^{\frac{2}{3}} + C

\frac{10}{s \cdot ( s + 1 ) \cdot ( s + 10 )}

2 t

\frac{\partial}{\partial x} (cos (2 x + 6 y))

\int t cos (a t) d t

\int tan^{4} (x se) c^{6} x d x

What is the integral of x/(\sqrt[3]{x+10)} ?
The integral of x/(\sqrt[3]{x+10)} is 3/5 (x+10)^{5/3}-15(x+10)^{2/3}+C