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Popular Calculus >

integral of sin^{10}(x)

Solution

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

Solution

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

Solution steps

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

Apply Integral Reduction

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

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

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

Add a constant to the solution

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

Graph

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Frequently Asked Questions (FAQ)

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