What is the integral of (x^8)/((25-x^2)^{11/2)} ?

The integral of (x^8)/((25-x^2)^{11/2)} is

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integral of (x^8)/((25-x^2)^{11/2)}

\int \frac{x ^{8}}{( 25 - x ^{2} ) ^{\frac{11}{2}}} d x

\frac{x ^{9}}{9 ( 25 - x ^{2} ) ^{\frac{11}{2}}} - \frac{- 5 ^{15} x ^{15} + 1525878906250 x ^{13} - 1.90735 E 13 x ^{11}}{6866455078125 ( x + 5 ) ( x - 5 ) ( - x ^{2} + 25 ) ^{\frac{13}{2}}} + C

Solution steps

\int \frac{x ^{8}}{( 25 - x ^{2} ) ^{\frac{11}{2}}} d x

Apply Integration By Parts

= \frac{x ^{9}}{9 ( 25 - x ^{2} ) ^{\frac{11}{2}}} - \int \frac{11 x ^{10}}{9 ( 25 - x ^{2} ) ^{\frac{13}{2}}} d x

\int \frac{11 x ^{10}}{9 ( 25 - x ^{2} ) ^{\frac{13}{2}}} d x = \frac{- 5 ^{15} x ^{15} + 1525878906250 x ^{13} - 1.90735 E 13 x ^{11}}{6866455078125 ( x + 5 ) ( x - 5 ) ( - x ^{2} + 25 ) ^{\frac{13}{2}}}

= \frac{x ^{9}}{9 ( 25 - x ^{2} ) ^{\frac{11}{2}}} - \frac{- 5 ^{15} x ^{15} + 1525878906250 x ^{13} - 1.90735 E 13 x ^{11}}{6866455078125 ( x + 5 ) ( x - 5 ) ( - x ^{2} + 25 ) ^{\frac{13}{2}}}

Add a constant to the solution

= \frac{x ^{9}}{9 ( 25 - x ^{2} ) ^{\frac{11}{2}}} - \frac{- 5 ^{15} x ^{15} + 1525878906250 x ^{13} - 1.90735 E 13 x ^{11}}{6866455078125 ( x + 5 ) ( x - 5 ) ( - x ^{2} + 25 ) ^{\frac{13}{2}}} + C

What is the integral of (x^8)/((25-x^2)^{11/2)} ?
The integral of (x^8)/((25-x^2)^{11/2)} is