integral of xsin^3(x)cos(x)

Lösung

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

\frac{1}{4} x sin^{4} (x) - \frac{1}{4} (- \frac{1}{4} sin^{3} (x) cos (x) + \frac{3}{8} (x - \frac{1}{2} sin (2 x))) + C

Schritte zur Lösung

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

Wende die partielle Integration an

= \frac{1}{4} x sin^{4} (x) - \int \frac{1}{4} sin^{4} (x) d x

\int \frac{1}{4} sin^{4} (x) d x = \frac{1}{4} (- \frac{1}{4} sin^{3} (x) cos (x) + \frac{3}{8} (x - \frac{1}{2} sin (2 x)))

= \frac{1}{4} x sin^{4} (x) - \frac{1}{4} (- \frac{1}{4} sin^{3} (x) cos (x) + \frac{3}{8} (x - \frac{1}{2} sin (2 x)))

Füge eine Konstante zur Lösung hinzu

= \frac{1}{4} x sin^{4} (x) - \frac{1}{4} (- \frac{1}{4} sin^{3} (x) cos (x) + \frac{3}{8} (x - \frac{1}{2} sin (2 x))) + C

\frac{d}{d x} ((x + 1) (2 x + 5)^{4})

\int e^{- \frac{x}{2}} d x

d er i v a t i v e \frac{x ^{2} - 6 x}{x + 1}

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

\frac{d}{d x} (x cos (x) - sin (x) ln (cos (x)))