integral of x^2sin(5/2)x^3sin(3/5)x^3

Lösung

\int x^{2} sin (\frac{5}{2}) x^{3} sin (\frac{3}{5}) x^{3} d x

\frac{1}{9} sin (\frac{5}{2}) sin (\frac{3}{5}) x^{9} + C

Schritte zur Lösung

\int x^{2} sin (\frac{5}{2}) x^{3} sin (\frac{3}{5}) x^{3} d x

Entferne die Konstante:

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

= sin (\frac{5}{2}) sin (\frac{3}{5}) \cdot \int x^{2} x^{3} x^{3} d x

Vereinfache

x^{2} x^{3} x^{3} : x^{8}

= sin (\frac{5}{2}) sin (\frac{3}{5}) \cdot \int x^{8} d x

Wende die Potenzregel an

= sin (\frac{5}{2}) sin (\frac{3}{5}) \frac{x ^{9}}{9}

Vereinfache

sin (\frac{5}{2}) sin (\frac{3}{5}) \frac{x ^{9}}{9} : \frac{1}{9} sin (\frac{5}{2}) sin (\frac{3}{5}) x^{9}

= \frac{1}{9} sin (\frac{5}{2}) sin (\frac{3}{5}) x^{9}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{9} sin (\frac{5}{2}) sin (\frac{3}{5}) x^{9} + C

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