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Beliebt Rechnen >

integral of (x^2)arcsin(x)

Lösung

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

Lösung

\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

Graph

Beliebte Beispiele

integral of (2y^2)

\int (2 y^{2}) d y

integral of r/(sqrt(a^2-r^2))

\int \frac{r}{a ^{2} - r ^{2}} d r

integral from-1 to 2 of x(1+x^3)

\int_{- 1}^{2} x (1 + x^{3}) d x

derivative of 1/10 (x-60^2+100)

\frac{d}{d x} (\frac{1}{10} (x - 60)^{2} + 100)

taylor sin^2(x)

t a y l or sin^{2} (x)