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Beliebt Rechnen >

integral of (7-5x)sin(3-2x)

Lösung

\int (7 - 5 x) sin (3 - 2 x) d x

Lösung

\frac{7}{2} cos (3 - 2 x) - 5 (\frac{1}{2} x cos (3 - 2 x) + \frac{1}{4} sin (3 - 2 x)) + C

Schritte zur Lösung

\int (7 - 5 x) sin (3 - 2 x) d x

Multipliziere aus

(7 - 5 x) sin (3 - 2 x) : 7 sin (3 - 2 x) - 5 x sin (3 - 2 x)

= \int 7 sin (3 - 2 x) - 5 x sin (3 - 2 x) d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 7 sin (3 - 2 x) d x - \int 5 x sin (3 - 2 x) d x

\int 7 sin (3 - 2 x) d x = \frac{7}{2} cos (3 - 2 x)

\int 5 x sin (3 - 2 x) d x = 5 (\frac{1}{2} x cos (3 - 2 x) + \frac{1}{4} sin (3 - 2 x))

= \frac{7}{2} cos (3 - 2 x) - 5 (\frac{1}{2} x cos (3 - 2 x) + \frac{1}{4} sin (3 - 2 x))

Füge eine Konstante zur Lösung hinzu

= \frac{7}{2} cos (3 - 2 x) - 5 (\frac{1}{2} x cos (3 - 2 x) + \frac{1}{4} sin (3 - 2 x)) + C

Graph

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