integral of xcos^2(x)

Lösung

\int x cos^{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 cos^{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

y^{^{'}} - x y^{2} = 2 x y

t \to 0 + lim (t (ln (t))^{2})

d er i v a t i v e 3 cos^{2} (x)

\frac{d}{d x} (2 sin (x) + cos (x))

(x - 2)^{^{'}}