integral of cot^5(2/5)xcsc^9(2/5)x

Lösung

\int cot^{5} (\frac{2}{5}) x csc^{9} (\frac{2}{5}) x d x

\frac{csc ^{9} ( \frac{2}{5} ) cot ^{5} ( \frac{2}{5} ) x ^{3}}{3} + C

Schritte zur Lösung

\int cot^{5} (\frac{2}{5}) x csc^{9} (\frac{2}{5}) x d x

Entferne die Konstante:

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

= cot^{5} (\frac{2}{5}) csc^{9} (\frac{2}{5}) \cdot \int xx d x

Vereinfache

xx : x^{2}

= cot^{5} (\frac{2}{5}) csc^{9} (\frac{2}{5}) \cdot \int x^{2} d x

Wende die Potenzregel an

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

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Füge eine Konstante zur Lösung hinzu

= \frac{csc ^{9} ( \frac{2}{5} ) cot ^{5} ( \frac{2}{5} ) x ^{3}}{3} + C

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