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

Lösung

\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

Schritte zur Lösung

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

Wende die partielle Integration an

= \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}}}

Füge eine Konstante zur Lösung hinzu

= \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

\int 1 \frac{1}{1 + x ^{2}} d x

\int 15 - x^{2} 9 x d x

\int sin (30) d x

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

\int csc^{2} (x) cot^{3} (x) d x