What is the integral of cos^6(θ) ?

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

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integral of cos^6(θ)

\int cos^{6} (θ) d θ

\frac{sin ( θ ) cos ^{5} ( θ )}{6} + \frac{5}{6} (\frac{1}{4} cos^{3} (θ) sin (θ) + \frac{3}{8} (θ + \frac{1}{2} sin (2 θ))) + C

Solution steps

\int cos^{6} (θ) d θ

Apply Integral Reduction

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

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

= \frac{sin ( θ ) cos ^{5} ( θ )}{6} + \frac{5}{6} (\frac{1}{4} cos^{3} (θ) sin (θ) + \frac{3}{8} (θ + \frac{1}{2} sin (2 θ)))

Add a constant to the solution

= \frac{sin ( θ ) cos ^{5} ( θ )}{6} + \frac{5}{6} (\frac{1}{4} cos^{3} (θ) sin (θ) + \frac{3}{8} (θ + \frac{1}{2} sin (2 θ))) + C

\frac{d}{d x} (3 - 4 x^{2})

f (x) = (x - x^{3}), at x = 1

\frac{d}{d x} (\frac{1}{4} e^{2 x})

\int (sin (3 x) + 3 cos (3 x))^{2} d x

\frac{\partial}{\partial x} (2 x y^{7} + x^{7} y^{9})

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