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Beliebt Rechnen >

integral of arcsin(2x+2)

Lösung

\int arcsin (2 x + 2) d x

Lösung

x arcsin (2 x + 2) + \frac{1}{2} - 4 x^{2} - 8 x - 3 + arcsin (2 (x + 1)) + C

Schritte zur Lösung

\int arcsin (2 x + 2) d x

Wende die partielle Integration an

= x arcsin (2 x + 2) - \int \frac{2 x}{- 4 x ^{2} - 8 x - 3} d x

\int \frac{2 x}{- 4 x ^{2} - 8 x - 3} d x = - \frac{1}{2} - 4 x^{2} - 8 x - 3 - arcsin (2 (x + 1))

= x arcsin (2 x + 2) - (- \frac{1}{2} - 4 x^{2} - 8 x - 3 - arcsin (2 (x + 1)))

Vereinfache

= x arcsin (2 x + 2) + \frac{1}{2} - 4 x^{2} - 8 x - 3 + arcsin (2 (x + 1))

Füge eine Konstante zur Lösung hinzu

= x arcsin (2 x + 2) + \frac{1}{2} - 4 x^{2} - 8 x - 3 + arcsin (2 (x + 1)) + C

Graph

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