integral of sin^3(x)+cos^2(x)

Lösung

\int sin^{3} (x) + cos^{2} (x) d x

- cos (x) + \frac{cos ^{3} ( x )}{3} + \frac{1}{2} (x + \frac{1}{2} sin (2 x)) + C

Schritte zur Lösung

\int sin^{3} (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 sin^{3} (x) d x + \int cos^{2} (x) d x

\int sin^{3} (x) d x = - cos (x) + \frac{cos ^{3} ( x )}{3}

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

= - cos (x) + \frac{cos ^{3} ( x )}{3} + \frac{1}{2} (x + \frac{1}{2} sin (2 x))

Füge eine Konstante zur Lösung hinzu

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

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