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Beliebt Rechnen >

integral of e^{5x+3}sin(2x-1)

Lösung

\int e^{5 x + 3} sin (2 x - 1) d x

Lösung

- \frac{2 e ^{5 x + 3} cos ( 2 x - 1 )}{29} + \frac{5 e ^{5 x + 3} sin ( 2 x - 1 )}{29} + C

Schritte zur Lösung

\int e^{5 x + 3} sin (2 x - 1) d x

Wende die partielle Integration an

= - \frac{1}{2} e^{5 x + 3} cos (2 x - 1) - \int - \frac{5}{2} e^{5 x + 3} cos (2 x - 1) d x

Entferne die Konstante:

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

= - \frac{1}{2} e^{5 x + 3} cos (2 x - 1) - (- \frac{5}{2} \cdot \int e^{5 x + 3} cos (2 x - 1) d x)

Wende die partielle Integration an

= - \frac{1}{2} e^{5 x + 3} cos (2 x - 1) - (- \frac{5}{2} (\frac{1}{2} e^{5 x + 3} sin (2 x - 1) - \int \frac{5}{2} e^{5 x + 3} sin (2 x - 1) d x))

Entferne die Konstante:

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

= - \frac{1}{2} e^{5 x + 3} cos (2 x - 1) - (- \frac{5}{2} (\frac{1}{2} e^{5 x + 3} sin (2 x - 1) - \frac{5}{2} \cdot \int e^{5 x + 3} sin (2 x - 1) d x))

Deshalb

\int e^{5 x + 3} sin (2 x - 1) d x = - \frac{1}{2} e^{5 x + 3} cos (2 x - 1) - (- \frac{5}{2} (\frac{1}{2} e^{5 x + 3} sin (2 x - 1) - \frac{5}{2} \cdot \int e^{5 x + 3} sin (2 x - 1) d x))

Isoliere

\int e^{5 x + 3} sin (2 x - 1) d x

= - \frac{2 e ^{5 x + 3} cos ( 2 x - 1 )}{29} + \frac{5 e ^{5 x + 3} sin ( 2 x - 1 )}{29}

Füge eine Konstante zur Lösung hinzu

= - \frac{2 e ^{5 x + 3} cos ( 2 x - 1 )}{29} + \frac{5 e ^{5 x + 3} sin ( 2 x - 1 )}{29} + C

Graph

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