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Popular >

integral of csc^9(x)

Solution

\int csc^{9} (x) d x

Solution

- \frac{cos ( x ) csc ^{8} ( x )}{8} + \frac{7}{8} (- \frac{1}{6} csc^{6} (x) cos (x) + \frac{5}{48} (- 2 csc^{4} (x) cos (x) + 3 (- cot (x) csc (x) + ln tan (\frac{x}{2})))) + C

Solution steps

\int csc^{9} (x) d x

Apply Integral Reduction

= - \frac{cos ( x ) csc ^{8} ( x )}{8} + \frac{7}{8} \cdot \int csc^{7} (x) d x

\int csc^{7} (x) d x = - \frac{1}{6} csc^{6} (x) cos (x) + \frac{5}{48} (- 2 csc^{4} (x) cos (x) + 3 (- cot (x) csc (x) + ln tan (\frac{x}{2})))

= - \frac{cos ( x ) csc ^{8} ( x )}{8} + \frac{7}{8} (- \frac{1}{6} csc^{6} (x) cos (x) + \frac{5}{48} (- 2 csc^{4} (x) cos (x) + 3 (- cot (x) csc (x) + ln tan (\frac{x}{2}))))

Add a constant to the solution

= - \frac{cos ( x ) csc ^{8} ( x )}{8} + \frac{7}{8} (- \frac{1}{6} csc^{6} (x) cos (x) + \frac{5}{48} (- 2 csc^{4} (x) cos (x) + 3 (- cot (x) csc (x) + ln tan (\frac{x}{2})))) + C

Popular Examples

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integral of x^{27}e^{x^{28}}

\int x^{27} e^{x^{28}} d x

integral of cos^4(7x+8)

\int cos^{4} (7 x + 8) d x

Frequently Asked Questions (FAQ)

What is the integral of csc^9(x) ?
The integral of csc^9(x) is