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Beliebt Rechnen >

integral of (xarcsin(x))/(sqrt(1-x^2))

Lösung

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

Lösung

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

Schritte zur Lösung

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

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

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

Wende die partielle Integration an

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

\int - 1 d x = - x

= - arcsin (x) 1 - x^{2} - (- x)

Vereinfache

= - arcsin (x) 1 - x^{2} + x

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of x^i

\int x^{i} d x

integral of ((x+2))/(x+1)

\int \frac{( x + 2 )}{x + 1} d x

limit as x approaches 1 of (x-1)/(x^2+1)

x \to 1 lim (\frac{x - 1}{x ^{2} + 1})

integral of sqrt(6x+3)

\int 6 x + 3 d x

sum from n=1 to infinity of 1/(e^{n^3)}

n = 1 \sum \infty \frac{1}{e ^{n^{3}}}