integral of x^5sin(x)

Lösung

\int x^{5} sin (x) d x

- x^{5} cos (x) + 5 (x^{4} sin (x) - 4 (- x^{3} cos (x) + 3 (x^{2} sin (x) - 2 (- x cos (x) + sin (x))))) + C

Schritte zur Lösung

\int x^{5} sin (x) d x

Wende die partielle Integration an

= - x^{5} cos (x) - \int - 5 x^{4} cos (x) d x

\int - 5 x^{4} cos (x) d x = - 5 (x^{4} sin (x) - 4 (- x^{3} cos (x) + 3 (x^{2} sin (x) - 2 (- x cos (x) + sin (x)))))

= - x^{5} cos (x) - (- 5 (x^{4} sin (x) - 4 (- x^{3} cos (x) + 3 (x^{2} sin (x) - 2 (- x cos (x) + sin (x))))))

Vereinfache

= - x^{5} cos (x) + 5 (x^{4} sin (x) - 4 (- x^{3} cos (x) + 3 (x^{2} sin (x) - 2 (- x cos (x) + sin (x)))))

Füge eine Konstante zur Lösung hinzu

= - x^{5} cos (x) + 5 (x^{4} sin (x) - 4 (- x^{3} cos (x) + 3 (x^{2} sin (x) - 2 (- x cos (x) + sin (x))))) + C

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

d er i v a t i v e f (x) = 3 x ln (5 x) - 3 x

(1 + x^{2}) y^{^{'}} - 2 x y = x^{2} + x^{4}

a re a y = x^{4} + x^{3}, y = x^{4} + x^{2} + 6 x

\frac{d}{d x} (A e^{4 x})