What is the integral of cos^6(x) ?

The integral of cos^6(x) is (sin(x)cos^5(x))/6+5/6 (1/4 cos^3(x)sin(x)+3/8 (x+1/2 sin(2x)))+C

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integral of cos^6(x)

integral

cos^{6} (x)

\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^{6} (x) d x

Apply Integral Reduction

= \frac{sin ( x ) cos ^{5} ( x )}{6} + \frac{5}{6} \cdot \int cos^{4} (x) d x

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

= \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 ^{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

\frac{1}{a ^{x}}

\frac{1}{( x ^{2} + 2 )}

\frac{x ^{2}}{( x ^{3} + 1 )}

\frac{x}{( x + 2 )}

\frac{( 2 x )}{( 1 + 4 x ^{2} )}

What is the integral of cos^6(x) ?
The integral of cos^6(x) is (sin(x)cos^5(x))/6+5/6 (1/4 cos^3(x)sin(x)+3/8 (x+1/2 sin(2x)))+C