integral of xcos(1/2)x

Lösung

\int x cos (\frac{1}{2}) x d x

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

Schritte zur Lösung

\int x cos (\frac{1}{2}) x d x

Entferne die Konstante:

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

= cos (\frac{1}{2}) \cdot \int xx d x

Vereinfache

xx : x^{2}

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

Wende die Potenzregel an

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

Vereinfache

cos (\frac{1}{2}) \frac{x ^{3}}{3} : \frac{1}{3} cos (\frac{1}{2}) x^{3}

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

Füge eine Konstante zur Lösung hinzu

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

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