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Beliebt Rechnen >

integral of x^3sin(4x^4-pi)

Lösung

\int x^{3} sin (4 x^{4} - π) d x

Lösung

\frac{1}{16} cos (4 x^{4}) + C

Schritte zur Lösung

\int x^{3} sin (4 x^{4} - π) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

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

Entferne die Konstante:

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

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

Wende die partielle Integration an

= - (\frac{1}{4} x^{4} sin (4 x^{4}) - \int 4 x^{7} cos (4 x^{4}) d x)

\int 4 x^{7} cos (4 x^{4}) d x = \frac{1}{16} (4 x^{4} sin (4 x^{4}) + cos (4 x^{4}))

= - (\frac{1}{4} x^{4} sin (4 x^{4}) - \frac{1}{16} (4 x^{4} sin (4 x^{4}) + cos (4 x^{4})))

Vereinfache

- (\frac{1}{4} x^{4} sin (4 x^{4}) - \frac{1}{16} (4 x^{4} sin (4 x^{4}) + cos (4 x^{4}))) : \frac{1}{16} cos (4 x^{4})

= \frac{1}{16} cos (4 x^{4})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{16} cos (4 x^{4}) + C

Graph

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