integral of arcsin(x-1)

Lösung

\int arcsin (x - 1) d x

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

Schritte zur Lösung

\int arcsin (x - 1) d x

Wende die partielle Integration an

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

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