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Beliebt Rechnen >

integral of (sin(2x))/(sqrt(sin^2(x)-3))

Lösung

\int \frac{sin ( 2 x )}{sin ^{2} ( x ) - 3} d x

Lösung

2 sin^{2} (x) - 3 + C

Schritte zur Lösung

\int \frac{sin ( 2 x )}{sin ^{2} ( x ) - 3} d x

Wende U-Substitution an

= \int \frac{1}{u} d u

Wende die Potenzregel an

= 2 u^{\frac{1}{2}}

Setze in

u = sin^{2} (x) - 3

ein

= 2 (sin^{2} (x) - 3)^{\frac{1}{2}}

Wende Radikal Regel an:

a^{\frac{1}{n}} = n a

= 2 sin^{2} (x) - 3

Füge eine Konstante zur Lösung hinzu

= 2 sin^{2} (x) - 3 + C

Graph

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