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

The integral of (3sqrt(x)-2\sqrt[3]{x}) is 2x^{3/2}-3/2 x^{4/3}+C

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

\int (3 x - 2 3 x) d x

2 x^{\frac{3}{2}} - \frac{3}{2} x^{\frac{4}{3}} + C

Solution steps

\int 3 x - 2 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 3 x d x - \int 2 3 x d x

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

\int 2 3 x d x = \frac{3}{2} x^{\frac{4}{3}}

= 2 x^{\frac{3}{2}} - \frac{3}{2} x^{\frac{4}{3}}

Add a constant to the solution

= 2 x^{\frac{3}{2}} - \frac{3}{2} x^{\frac{4}{3}} + C

5

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

\frac{d}{d x} (\frac{tan ( x )}{6 x sec ( x )})

\frac{\partial}{\partial x} (se x)

5 y^{^{''}} - 4 y = 0

What is the integral of (3sqrt(x)-2\sqrt[3]{x}) ?
The integral of (3sqrt(x)-2\sqrt[3]{x}) is 2x^{3/2}-3/2 x^{4/3}+C