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Beliebt Rechnen >

integral of x+cos^2(x)

Lösung

\int x + cos^{2} (x) d x

Lösung

\frac{x ^{2}}{2} + \frac{1}{2} (x + \frac{1}{2} sin (2 x)) + C

Schritte zur Lösung

\int x + cos^{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 x d x + \int cos^{2} (x) d x

\int x d x = \frac{x ^{2}}{2}

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

= \frac{x ^{2}}{2} + \frac{1}{2} (x + \frac{1}{2} sin (2 x))

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{2} + \frac{1}{2} (x + \frac{1}{2} sin (2 x)) + C

Graph

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