integral of cot(θ)*ln(7sin(θ))

Lösung

\int cot (θ) \cdot ln (7 sin (θ)) d θ

ln (7 sin (θ)) ln ∣ sin (θ) ∣ - \frac{ln ∣ sin ( θ ) ∣ ^{2}}{2} + C

Schritte zur Lösung

\int cot (θ) ln (7 sin (θ)) d θ

Wende die partielle Integration an

= ln (7 sin (θ)) ln ∣ sin (θ) ∣ - \int cot (θ) ln ∣ sin (θ) ∣ d θ

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

= ln (7 sin (θ)) ln ∣ sin (θ) ∣ - \frac{ln ∣ sin ( θ ) ∣ ^{2}}{2}

Füge eine Konstante zur Lösung hinzu

= ln (7 sin (θ)) ln ∣ sin (θ) ∣ - \frac{ln ∣ sin ( θ ) ∣ ^{2}}{2} + C

\int \frac{x + sin ( x )}{1 + sin ( x )} d x

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\int (5 x - 2)^{9} d x