integral of arcsin(x)x

Lösung

\int arcsin (x) x d x

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

Schritte zur Lösung

\int arcsin (x) x d x

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

x \to - 3 lim (2 x^{3} + 5 x^{2} - 25)

y^{^{'}} = \frac{2 y}{x}, y (1) = 2

\int_{0}^{1} \frac{x}{e ^{2 x}} d x

d er i v a t i v e - 9.8 x^{2} + 2 x + 1

\int_{1}^{2} \frac{4}{2 x + 3} d x