What is the integral of (\sqrt[3]{x^2})/3 ?

The integral of (\sqrt[3]{x^2})/3 is 1/5 x^{5/3}+C

Popular >

integral of (\sqrt[3]{x^2})/3

\int \frac{3 x ^{2}}{3} d x

\frac{1}{5} x^{\frac{5}{3}} + C

Solution steps

\int \frac{3 x ^{2}}{3} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int 3 x^{2} d x

3 x^{2} = x^{\frac{2}{3}},

assuming

x \geq 0

= \frac{1}{3} \cdot \int x^{\frac{2}{3}} d x

Apply the Power Rule

: \frac{3}{5} x^{\frac{5}{3}}

= \frac{1}{3} \cdot \frac{3}{5} x^{\frac{5}{3}}

Simplify

\frac{1}{3} \cdot \frac{3}{5} x^{\frac{5}{3}} : \frac{1}{5} x^{\frac{5}{3}}

= \frac{1}{5} x^{\frac{5}{3}}

Add a constant to the solution

= \frac{1}{5} x^{\frac{5}{3}} + C

\int 4 (3 x - 2)^{3} d x

\int 7^{(2 x + 3)} d x

\int \frac{4}{x ln ( 2 x )} d x

\int \frac{1}{x} e^{1 + l n (x)} d x

\int 7 sin^{2} (x) cos (x) d x

What is the integral of (\sqrt[3]{x^2})/3 ?
The integral of (\sqrt[3]{x^2})/3 is 1/5 x^{5/3}+C