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Beliebt Rechnen >

integral of cos(θ)sqrt(sin(θ)+1)

Lösung

\int cos (θ) sin (θ) + 1 d θ

Lösung

sin (θ) sin (θ) + 1 - \frac{1}{3} (sin (θ) + 1)^{\frac{3}{2}} + sin (θ) + 1 + C

Schritte zur Lösung

\int cos (θ) sin (θ) + 1 d θ

Wende die partielle Integration an

= sin (θ) sin (θ) + 1 - \int \frac{cos ( θ ) sin ( θ )}{2 sin ( θ ) + 1} d θ

\int \frac{cos ( θ ) sin ( θ )}{2 sin ( θ ) + 1} d θ = \frac{1}{3} (sin (θ) + 1)^{\frac{3}{2}} - sin (θ) + 1

= sin (θ) sin (θ) + 1 - (\frac{1}{3} (sin (θ) + 1)^{\frac{3}{2}} - sin (θ) + 1)

Vereinfache

= sin (θ) sin (θ) + 1 - \frac{1}{3} (sin (θ) + 1)^{\frac{3}{2}} + sin (θ) + 1

Füge eine Konstante zur Lösung hinzu

= sin (θ) sin (θ) + 1 - \frac{1}{3} (sin (θ) + 1)^{\frac{3}{2}} + sin (θ) + 1 + C

Graph

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