What is the integral of cot^5(2/5)xcsc^9(2/5)x ?

The integral of cot^5(2/5)xcsc^9(2/5)x is (csc^9(2/5)cot^5(2/5)x^3)/3+C

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

\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

Solution steps

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

Take the constant out:

\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

Simplify

xx : x^{2}

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

Apply the Power Rule

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

Multiply fractions:

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

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

Add a constant to the solution

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

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What is the integral of cot^5(2/5)xcsc^9(2/5)x ?
The integral of cot^5(2/5)xcsc^9(2/5)x is (csc^9(2/5)cot^5(2/5)x^3)/3+C