integral of x*sin^2(x)

Lösung

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\frac{d}{d x} (- 2 sin (x^{2}) - 4 x^{2} cos (x^{2}))

\int \frac{1}{x ^{2} + x - 12} d x

d er i v a t i v e t e^{- t}

\frac{d}{d x} (\frac{2 x ^{5} + 3 x ^{4} - 1}{- 2 x ^{7}})

\frac{d}{d θ} (- cos (θ))