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

The integral of sin(5θ)sin(θ) is 1/2 (-1/6 sin(6θ)+1/4 sin(4θ))+C

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integral of sin(5θ)sin(θ)

\int sin (5 θ) sin (θ) d θ

\frac{1}{2} (- \frac{1}{6} sin (6 θ) + \frac{1}{4} sin (4 θ)) + C

Solution steps

\int sin (5 θ) sin (θ) d θ

Rewrite using trig identities

= \int \frac{1}{2} (- cos (6 θ) + cos (4 θ)) d θ

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int - cos (6 θ) + cos (4 θ) d θ

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (- \int cos (6 θ) d θ + \int cos (4 θ) d θ)

\int cos (6 θ) d θ = \frac{1}{6} sin (6 θ)

\int cos (4 θ) d θ = \frac{1}{4} sin (4 θ)

= \frac{1}{2} (- \frac{1}{6} sin (6 θ) + \frac{1}{4} sin (4 θ))

Add a constant to the solution

= \frac{1}{2} (- \frac{1}{6} sin (6 θ) + \frac{1}{4} sin (4 θ)) + C

\frac{\partial}{\partial x} (9 x e^{4 x y})

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

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

n = 1 \sum \infty \frac{4 ^{n}}{2 ^{n}}

x y - 3 y^{2} = 8, (14, 4)

What is the integral of sin(5θ)sin(θ) ?
The integral of sin(5θ)sin(θ) is 1/2 (-1/6 sin(6θ)+1/4 sin(4θ))+C