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Beliebt Rechnen >

integral of (cot(x))^4

Lösung

\int (cot (x))^{4} d x

Lösung

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

Schritte zur Lösung

\int (cot (x))^{4} d x

Vereinfache

= \int cot^{4} (x) d x

Wende integrale Reduktion an

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

\int cot^{2} (x) d x = - x - cot (x)

= - \frac{cot ^{3} ( x )}{3} - (- x - cot (x))

Vereinfache

- \frac{cot ^{3} ( x )}{3} - (- x - cot (x)) : - \frac{1}{3} cot^{3} (x) + x + cot (x)

= - \frac{1}{3} cot^{3} (x) + x + cot (x)

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (x^2)/(sqrt(4x^2-9))

\int \frac{x ^{2}}{4 x ^{2} - 9} d x

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\int \frac{x ^{3} + 3 x ^{2} + 2 x + 5}{x + 2} d x

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\int sin (\frac{π}{6} x) d x

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