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Beliebt Rechnen >

integral of x*arcsin(x)

Lösung

\int x \cdot arcsin (x) d x

Lösung

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

Schritte zur Lösung

\int x arcsin (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

Graph

Beliebte Beispiele

erweitern (x^2+x^3)^4

e x p an d (x^{2} + x^{3})^{4}

integral of t/((t^2+1)^{7/2)}

\int \frac{t}{( t ^{2} + 1 ) ^{\frac{7}{2}}} d t

fläche y=2x^2-1,(0,3)

a re a y = 2 x^{2} - 1, (0, 3)

y^{''}+4y^'+4y=4e^{-2t}

y^{^{''}} + 4 y^{^{'}} + 4 y = 4 e^{- 2 t}

integral of ((x-3))/((x+4)(x-5))

\int \frac{( x - 3 )}{( x + 4 ) ( x - 5 )} d x