integral of-x^3sin(x)

Lösung

\int - x^{3} sin (x) d x

x^{3} cos (x) - 3 x^{2} sin (x) - 6 x cos (x) + 6 sin (x) + C

Schritte zur Lösung

\int - x^{3} sin (x) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int x^{3} sin (x) d x

Wende die partielle Integration an

= - (- x^{3} cos (x) - \int - 3 x^{2} cos (x) d x)

\int - 3 x^{2} cos (x) d x = - 3 (x^{2} sin (x) - 2 (- x cos (x) + sin (x)))

= - (- x^{3} cos (x) - (- 3 (x^{2} sin (x) - 2 (- x cos (x) + sin (x)))))

Vereinfache

- (- x^{3} cos (x) - (- 3 (x^{2} sin (x) - 2 (- x cos (x) + sin (x))))) : x^{3} cos (x) - 3 x^{2} sin (x) - 6 x cos (x) + 6 sin (x)

= x^{3} cos (x) - 3 x^{2} sin (x) - 6 x cos (x) + 6 sin (x)

Füge eine Konstante zur Lösung hinzu

= x^{3} cos (x) - 3 x^{2} sin (x) - 6 x cos (x) + 6 sin (x) + C

\int \frac{x ^{3}}{x ^{2} - 64} d x

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

\int \frac{12}{( x - 4 ) ( x + 8 )} d x

\int \frac{cos ( x ^{- 1} )}{x ^{2}} d x

\int \frac{x ^{2} + 2}{3} d x