integral of cot(x)ln(csc(x))

Lösung

\int cot (x) ln (csc (x)) d x

ln (csc (x)) ln ∣ sin (x) ∣ + \frac{1}{2} ln ∣ sin (x) ∣^{2} + C

Schritte zur Lösung

\int cot (x) ln (csc (x)) d x

Wende die partielle Integration an

= ln (csc (x)) ln ∣ sin (x) ∣ - \int - cot (x) ln ∣ sin (x) ∣ d x

\int - cot (x) ln ∣ sin (x) ∣ d x = - \frac{ln ∣ sin ( x ) ∣ ^{2}}{2}

= ln (csc (x)) ln ∣ sin (x) ∣ - (- \frac{ln ∣ sin ( x ) ∣ ^{2}}{2})

Vereinfache

ln (csc (x)) ln ∣ sin (x) ∣ - (- \frac{ln ∣ sin ( x ) ∣ ^{2}}{2}) : ln (csc (x)) ln ∣ sin (x) ∣ + \frac{1}{2} ln ∣ sin (x) ∣^{2}

= ln (csc (x)) ln ∣ sin (x) ∣ + \frac{1}{2} ln ∣ sin (x) ∣^{2}

Füge eine Konstante zur Lösung hinzu

= ln (csc (x)) ln ∣ sin (x) ∣ + \frac{1}{2} ln ∣ sin (x) ∣^{2} + C

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