What is the integral of 2/5 x^{5/2}-54/5 ?

The integral of 2/5 x^{5/2}-54/5 is 4/35 x^{7/2}-54/5 x+C

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integral of 2/5 x^{5/2}-54/5

\int \frac{2}{5} x^{\frac{5}{2}} - \frac{54}{5} d x

\frac{4}{35} x^{\frac{7}{2}} - \frac{54}{5} x + C

Solution steps

\int \frac{2}{5} x^{\frac{5}{2}} - \frac{54}{5} 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 \frac{2}{5} x^{\frac{5}{2}} d x - \int \frac{54}{5} d x

\int \frac{2}{5} x^{\frac{5}{2}} d x = \frac{4}{35} x^{\frac{7}{2}}

\int \frac{54}{5} d x = \frac{54}{5} x

= \frac{4}{35} x^{\frac{7}{2}} - \frac{54}{5} x

Add a constant to the solution

= \frac{4}{35} x^{\frac{7}{2}} - \frac{54}{5} x + C

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What is the integral of 2/5 x^{5/2}-54/5 ?
The integral of 2/5 x^{5/2}-54/5 is 4/35 x^{7/2}-54/5 x+C