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Beliebt Rechnen >

integral of e^{5θ}sin(6θ)

Lösung

\int e^{5 θ} sin (6 θ) d θ

Lösung

- \frac{6 e ^{5 θ} cos ( 6 θ )}{61} + \frac{5 e ^{5 θ} sin ( 6 θ )}{61} + C

Schritte zur Lösung

\int e^{5 θ} sin (6 θ) d θ

Wende die partielle Integration an

= - \frac{1}{6} e^{5 θ} cos (6 θ) - \int - \frac{5}{6} e^{5 θ} cos (6 θ) d θ

Entferne die Konstante:

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

= - \frac{1}{6} e^{5 θ} cos (6 θ) - (- \frac{5}{6} \cdot \int e^{5 θ} cos (6 θ) d θ)

Wende die partielle Integration an

= - \frac{1}{6} e^{5 θ} cos (6 θ) - (- \frac{5}{6} (\frac{1}{6} e^{5 θ} sin (6 θ) - \int \frac{5}{6} e^{5 θ} sin (6 θ) d θ))

Entferne die Konstante:

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

= - \frac{1}{6} e^{5 θ} cos (6 θ) - (- \frac{5}{6} (\frac{1}{6} e^{5 θ} sin (6 θ) - \frac{5}{6} \cdot \int e^{5 θ} sin (6 θ) d θ))

Deshalb

\int e^{5 θ} sin (6 θ) d θ = - \frac{1}{6} e^{5 θ} cos (6 θ) - (- \frac{5}{6} (\frac{1}{6} e^{5 θ} sin (6 θ) - \frac{5}{6} \cdot \int e^{5 θ} sin (6 θ) d θ))

Isoliere

\int e^{5 θ} sin (6 θ) d θ

= - \frac{6 e ^{5 θ} cos ( 6 θ )}{61} + \frac{5 e ^{5 θ} sin ( 6 θ )}{61}

Füge eine Konstante zur Lösung hinzu

= - \frac{6 e ^{5 θ} cos ( 6 θ )}{61} + \frac{5 e ^{5 θ} sin ( 6 θ )}{61} + C

Graph

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