integral of x^3sin(5x)

Lösung

\int x^{3} sin (5 x) d x

- \frac{1}{5} x^{3} cos (5 x) + \frac{3}{625} (25 x^{2} sin (5 x) - 2 (- 5 x cos (5 x) + sin (5 x))) + C

Schritte zur Lösung

\int x^{3} sin (5 x) d x

Wende die partielle Integration an

= - \frac{1}{5} x^{3} cos (5 x) - \int - \frac{3}{5} x^{2} cos (5 x) d x

\int - \frac{3}{5} x^{2} cos (5 x) d x = - \frac{3}{625} (25 x^{2} sin (5 x) - 2 (- 5 x cos (5 x) + sin (5 x)))

= - \frac{1}{5} x^{3} cos (5 x) - (- \frac{3}{625} (25 x^{2} sin (5 x) - 2 (- 5 x cos (5 x) + sin (5 x))))

Vereinfache

= - \frac{1}{5} x^{3} cos (5 x) + \frac{3}{625} (25 x^{2} sin (5 x) - 2 (- 5 x cos (5 x) + sin (5 x)))

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{5} x^{3} cos (5 x) + \frac{3}{625} (25 x^{2} sin (5 x) - 2 (- 5 x cos (5 x) + sin (5 x))) + C

\int x \cdot sin (\frac{x}{2}) d x

t an g e n t 0.72 x^{3} - 4.8 x^{2} + 0.6 x + 7.6

d er i v a t i v e f (x) = 2 sin^{4} (x)

\int x^{2} + e^{x} d x

t an g e n t y = \frac{x}{8 x - 4}, at x = 2