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Beliebt Rechnen >

integral of csc^2(8θ)cot(8θ)

Lösung

\int csc^{2} (8 θ) cot (8 θ) d θ

Lösung

- \frac{1}{16} cot^{2} (8 θ) + C

Schritte zur Lösung

\int csc^{2} (8 θ) cot (8 θ) d θ

Wende U-Substitution an

= \int - \frac{u}{8} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \frac{1}{8} \cdot \int u d u

Wende die Potenzregel an

= - \frac{1}{8} \cdot \frac{u ^{2}}{2}

Setze in

u = cot (8 θ)

ein

= - \frac{1}{8} \cdot \frac{cot ^{2} ( 8 θ )}{2}

Vereinfache

- \frac{1}{8} \cdot \frac{cot ^{2} ( 8 θ )}{2} : - \frac{1}{16} cot^{2} (8 θ)

= - \frac{1}{16} cot^{2} (8 θ)

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{16} cot^{2} (8 θ) + C

Graph

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