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Popular >

integral of cos^{10}(x)

Solution

\int cos^{10} (x) d x

Solution

\frac{sin ( x ) cos ^{9} ( x )}{10} + \frac{9}{10} (\frac{sin ( x ) cos ^{7} ( x )}{8} + \frac{7}{8} (\frac{sin ( x ) cos ^{5} ( x )}{6} + \frac{5}{6} (\frac{1}{4} cos^{3} (x) sin (x) + \frac{3}{8} (x + \frac{1}{2} sin (2 x))))) + C

Solution steps

\int cos^{10} (x) d x

Apply Integral Reduction

= \frac{sin ( x ) cos ^{9} ( x )}{10} + \frac{9}{10} \cdot \int cos^{8} (x) d x

\int cos^{8} (x) d x = \frac{sin ( x ) cos ^{7} ( x )}{8} + \frac{7}{8} (\frac{sin ( x ) cos ^{5} ( x )}{6} + \frac{5}{6} (\frac{1}{4} cos^{3} (x) sin (x) + \frac{3}{8} (x + \frac{1}{2} sin (2 x))))

= \frac{sin ( x ) cos ^{9} ( x )}{10} + \frac{9}{10} (\frac{sin ( x ) cos ^{7} ( x )}{8} + \frac{7}{8} (\frac{sin ( x ) cos ^{5} ( x )}{6} + \frac{5}{6} (\frac{1}{4} cos^{3} (x) sin (x) + \frac{3}{8} (x + \frac{1}{2} sin (2 x)))))

Add a constant to the solution

= \frac{sin ( x ) cos ^{9} ( x )}{10} + \frac{9}{10} (\frac{sin ( x ) cos ^{7} ( x )}{8} + \frac{7}{8} (\frac{sin ( x ) cos ^{5} ( x )}{6} + \frac{5}{6} (\frac{1}{4} cos^{3} (x) sin (x) + \frac{3}{8} (x + \frac{1}{2} sin (2 x))))) + C

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Frequently Asked Questions (FAQ)

What is the integral of cos^{10}(x) ?
The integral of cos^{10}(x) is