What is the integral of (x^{4/3}-3x^{5/2}) ?

The integral of (x^{4/3}-3x^{5/2}) is 3/7 x^{7/3}-6/7 x^{7/2}+C

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integral of (x^{4/3}-3x^{5/2})

\int (x^{\frac{4}{3}} - 3 x^{\frac{5}{2}}) d x

\frac{3}{7} x^{\frac{7}{3}} - \frac{6}{7} x^{\frac{7}{2}} + C

Solution steps

\int x^{\frac{4}{3}} - 3 x^{\frac{5}{2}} 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^{\frac{4}{3}} d x - \int 3 x^{\frac{5}{2}} d x

\int x^{\frac{4}{3}} d x = \frac{3}{7} x^{\frac{7}{3}}

\int 3 x^{\frac{5}{2}} d x = \frac{6}{7} x^{\frac{7}{2}}

= \frac{3}{7} x^{\frac{7}{3}} - \frac{6}{7} x^{\frac{7}{2}}

Add a constant to the solution

= \frac{3}{7} x^{\frac{7}{3}} - \frac{6}{7} x^{\frac{7}{2}} + C

\int_{0}^{2 π} sin^{2} (x co) s^{2} x

\frac{\partial}{\partial x} (x^{2} + y^{2} - 2 y + 1)

\frac{\partial}{\partial x} (y^{2} + 2 x^{2} - y)

\int_{1}^{2} \frac{1}{x ( ln ( x ) ) ^{p}} d x

f (x) = ln (3 x e^{- x})

What is the integral of (x^{4/3}-3x^{5/2}) ?
The integral of (x^{4/3}-3x^{5/2}) is 3/7 x^{7/3}-6/7 x^{7/2}+C