What is the integral of x(25-x)^{7/2} ?

The integral of x(25-x)^{7/2} is -2/9 x(25-x)^{9/2}-4/99 (25-x)^{11/2}+C

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integral of x(25-x)^{7/2}

\int x (25 - x)^{\frac{7}{2}} d x

- \frac{2}{9} x (25 - x)^{\frac{9}{2}} - \frac{4}{99} (25 - x)^{\frac{11}{2}} + C

Solution steps

\int x (25 - x)^{\frac{7}{2}} d x

Apply Integration By Parts

: - \frac{2}{9} x (25 - x)^{\frac{9}{2}} - \int - \frac{2}{9} (25 - x)^{\frac{9}{2}} d x

= - \frac{2}{9} x (25 - x)^{\frac{9}{2}} - \int - \frac{2}{9} (25 - x)^{\frac{9}{2}} d x

\int - \frac{2}{9} (25 - x)^{\frac{9}{2}} d x = \frac{4}{99} (25 - x)^{\frac{11}{2}}

= - \frac{2}{9} x (25 - x)^{\frac{9}{2}} - \frac{4}{99} (25 - x)^{\frac{11}{2}}

Add a constant to the solution

= - \frac{2}{9} x (25 - x)^{\frac{9}{2}} - \frac{4}{99} (25 - x)^{\frac{11}{2}} + C

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What is the integral of x(25-x)^{7/2} ?
The integral of x(25-x)^{7/2} is -2/9 x(25-x)^{9/2}-4/99 (25-x)^{11/2}+C