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Beliebt Rechnen >

integral of (cos(x))/((sin^2(x))^{1/3)}

Lösung

\int \frac{cos ( x )}{( sin ^{2} ( x ) ) ^{\frac{1}{3}}} d x

Lösung

3 sin^{\frac{1}{3}} (x) + C

Schritte zur Lösung

\int \frac{cos ( x )}{( sin ^{2} ( x ) ) ^{\frac{1}{3}}} d x

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

angenommen

sin (x) \geq 0

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

Wende U-Substitution an

= \int \frac{1}{u ^{\frac{2}{3}}} d u

Wende die Potenzregel an

= 3 u^{\frac{1}{3}}

Setze in

u = sin (x)

ein

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

Füge eine Konstante zur Lösung hinzu

= 3 sin^{\frac{1}{3}} (x) + C

Graph

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\int cos (\frac{x}{y}) d x