What is the integral of sin(θ)sin(3θ)sin(5θ) ?

The integral of sin(θ)sin(3θ)sin(5θ) is

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integral of sin(θ)sin(3θ)sin(5θ)

\int sin (θ) sin (3 θ) sin (5 θ) d θ

sin (θ) \frac{1}{2} (\frac{1}{2} sin (2 θ) - \frac{1}{8} sin (8 θ)) - \frac{1}{2} (- \frac{1}{3} cos^{3} (θ) - \frac{1}{16} (- \frac{1}{9} cos (9 θ) - \frac{1}{7} cos (7 θ))) + C

Solution steps

\int sin (θ) sin (3 θ) sin (5 θ) d θ

Apply Integration By Parts

: sin (θ) \frac{1}{2} (\frac{1}{2} sin (2 θ) - \frac{1}{8} sin (8 θ)) - \int cos (θ) \frac{1}{2} (\frac{1}{2} sin (2 θ) - \frac{1}{8} sin (8 θ)) d θ

= sin (θ) \frac{1}{2} (\frac{1}{2} sin (2 θ) - \frac{1}{8} sin (8 θ)) - \int cos (θ) \frac{1}{2} (\frac{1}{2} sin (2 θ) - \frac{1}{8} sin (8 θ)) d θ

\int cos (θ) \frac{1}{2} (\frac{1}{2} sin (2 θ) - \frac{1}{8} sin (8 θ)) d θ = \frac{1}{2} (- \frac{1}{3} cos^{3} (θ) - \frac{1}{16} (- \frac{1}{9} cos (9 θ) - \frac{1}{7} cos (7 θ)))

= sin (θ) \frac{1}{2} (\frac{1}{2} sin (2 θ) - \frac{1}{8} sin (8 θ)) - \frac{1}{2} (- \frac{1}{3} cos^{3} (θ) - \frac{1}{16} (- \frac{1}{9} cos (9 θ) - \frac{1}{7} cos (7 θ)))

Add a constant to the solution

= sin (θ) \frac{1}{2} (\frac{1}{2} sin (2 θ) - \frac{1}{8} sin (8 θ)) - \frac{1}{2} (- \frac{1}{3} cos^{3} (θ) - \frac{1}{16} (- \frac{1}{9} cos (9 θ) - \frac{1}{7} cos (7 θ))) + C

x, at x = 100

2 t^{2}

\frac{d}{d x} (arctan (\frac{9}{x}))

f (x) = 5 x + 6, (6, 6)

\int (tan (3 x) + cot (3 x))^{2} d x

What is the integral of sin(θ)sin(3θ)sin(5θ) ?
The integral of sin(θ)sin(3θ)sin(5θ) is