integral of x*sin(x/2)

Lösung

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

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

s \to 1 lim (\frac{s ^{3} - 1}{s - 1})