integral of x^2arcsin(x)

Lösung

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

\frac{1}{3} x^{3} arcsin (x) - \frac{1}{3} (\frac{1}{3} (1 - x^{2})^{\frac{3}{2}} - 1 - x^{2}) + C

Schritte zur Lösung

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

Wende die partielle Integration an

= \frac{1}{3} x^{3} arcsin (x) - \int \frac{x ^{3}}{3 1 - x ^{2}} d x

\int \frac{x ^{3}}{3 1 - x ^{2}} d x = \frac{1}{3} (\frac{1}{3} (1 - x^{2})^{\frac{3}{2}} - 1 - x^{2})

= \frac{1}{3} x^{3} arcsin (x) - \frac{1}{3} (\frac{1}{3} (1 - x^{2})^{\frac{3}{2}} - 1 - x^{2})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} x^{3} arcsin (x) - \frac{1}{3} (\frac{1}{3} (1 - x^{2})^{\frac{3}{2}} - 1 - x^{2}) + C

\frac{d}{d x} (- \frac{2}{5 x})

\frac{d}{d x} (\frac{x + 2}{ln ( x )})

\frac{\partial}{\partial y} (e^{\frac{y}{x}} - \frac{e ^{\frac{y}{x}} y}{x})

\int_{0}^{1} x 1 - x d x

so l v e f or x, \frac{d ^{2} x}{d t ^{2}} + x = (t^{2} + t) sin (t)