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))

\int (cos^{6} (x)) d 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

e^{- x^{3}}

\int (\frac{2}{t} - \frac{3}{t ^{2}}) d t

\int \frac{4 ^{c o t (5 x)}}{sin ^{2} ( 5 x )} d x

\int \frac{1}{2 ( x + \frac{5}{4} ) ^{2} - \frac{33}{8}} d x

\int x^{2} - 9 x d x

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