integral of x^3cos(5x)

Lösung

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

\frac{1}{5} x^{3} sin (5 x) - \frac{3}{5} (- \frac{1}{5} x^{2} cos (5 x) + \frac{2}{125} (5 x sin (5 x) + cos (5 x))) + C

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int \frac{3}{5} x^{2} sin (5 x) d x = \frac{3}{5} (- \frac{1}{5} x^{2} cos (5 x) + \frac{2}{125} (5 x sin (5 x) + cos (5 x)))

= \frac{1}{5} x^{3} sin (5 x) - \frac{3}{5} (- \frac{1}{5} x^{2} cos (5 x) + \frac{2}{125} (5 x sin (5 x) + cos (5 x)))

Füge eine Konstante zur Lösung hinzu

= \frac{1}{5} x^{3} sin (5 x) - \frac{3}{5} (- \frac{1}{5} x^{2} cos (5 x) + \frac{2}{125} (5 x sin (5 x) + cos (5 x))) + C

\int 20 x^{9} d x

t an g e n t f (x) = 4 x - 1, at x = 16

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

y^{^{'}} = x + 6 y

\frac{d}{d x} (ln (\frac{x}{3}) + \frac{x - 3}{x})