What is the integral of sqrt(x)-1/(\sqrt[3]{x)} ?

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

Popular >

integral of sqrt(x)-1/(\sqrt[3]{x)}

\int x - \frac{1}{3 x} d x

\frac{2}{3} x^{\frac{3}{2}} - \frac{3}{2} x^{\frac{2}{3}} + C

Solution steps

\int x - \frac{1}{3 x} d x

Apply the Sum Rule:

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

= \int x d x - \int \frac{1}{3 x} d x

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

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

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

Add a constant to the solution

= \frac{2}{3} x^{\frac{3}{2}} - \frac{3}{2} x^{\frac{2}{3}} + C

\int sin (8 x) sin (2 x) d x

\int sin (x) \cdot cos (x) \cdot e^{s i n (x)} d x

\int (e^{x} \cdot cos (e^{x})) d x

\int (2 x - \frac{1}{x})^{2} d x

\int \frac{ln ( x )}{( ln ( x ) + 1 ) ^{2}} d x

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