integral of (cos(7x)-xsin(4)x^2)

Lösung

\int (cos (7 x) - x sin (4) x^{2}) d x

\frac{1}{7} sin (7 x) - \frac{1}{4} sin (4) x^{4} + C

Schritte zur Lösung

\int cos (7 x) - x sin (4) x^{2} 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 cos (7 x) d x - \int x sin (4) x^{2} d x

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

\int x sin (4) x^{2} d x = \frac{1}{4} sin (4) x^{4}

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

Füge eine Konstante zur Lösung hinzu

= \frac{1}{7} sin (7 x) - \frac{1}{4} sin (4) x^{4} + C

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