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

The integral of 3x^{5/2}-x^{5/3} is 6/7 x^{7/2}-3/8 x^{8/3}+C

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integral of 3x^{5/2}-x^{5/3}

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

\frac{6}{7} x^{\frac{7}{2}} - \frac{3}{8} x^{\frac{8}{3}} + C

Solution steps

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

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

\int x^{\frac{5}{3}} d x = \frac{3}{8} x^{\frac{8}{3}}

= \frac{6}{7} x^{\frac{7}{2}} - \frac{3}{8} x^{\frac{8}{3}}

Add a constant to the solution

= \frac{6}{7} x^{\frac{7}{2}} - \frac{3}{8} x^{\frac{8}{3}} + C

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What is the integral of 3x^{5/2}-x^{5/3} ?
The integral of 3x^{5/2}-x^{5/3} is 6/7 x^{7/2}-3/8 x^{8/3}+C