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Beliebt Rechnen >

integral of ln(x)-cos(4x)

Lösung

\int ln (x) - cos (4 x) d x

Lösung

x ln (x) - x - \frac{1}{4} sin (4 x) + C

Schritte zur Lösung

\int ln (x) - cos (4 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 ln (x) d x - \int cos (4 x) d x

\int ln (x) d x = x ln (x) - x

\int cos (4 x) d x = \frac{1}{4} sin (4 x)

= x ln (x) - x - \frac{1}{4} sin (4 x)

Füge eine Konstante zur Lösung hinzu

= x ln (x) - x - \frac{1}{4} sin (4 x) + C

Graph

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\int \frac{1}{s} e^{- s t} d t

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\int (3 - 4 x)^{8} d x

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\int \frac{1}{3} x e^{x} d x