What is the integral of sin(3)(θ)cos(6)(θ) ?

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

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integral of sin(3)(θ)cos(6)(θ)

\int sin (3) (θ) cos (6) (θ) d θ

\frac{1}{3} sin (3) cos (6) θ^{3} + C

Solution steps

\int sin (3) θ cos (6) θ d θ

Take the constant out:

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

= sin (3) cos (6) \cdot \int θθ d θ

Simplify

θθ : θ^{2}

= sin (3) cos (6) \cdot \int θ^{2} d θ

Apply the Power Rule

: \frac{θ ^{3}}{3}

= sin (3) cos (6) \frac{θ ^{3}}{3}

Simplify

sin (3) cos (6) \frac{θ ^{3}}{3} : \frac{1}{3} sin (3) cos (6) θ^{3}

= \frac{1}{3} sin (3) cos (6) θ^{3}

Add a constant to the solution

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

\int_{0}^{1} x e^{- 5 x^{2}} d x

\int_{0}^{1} \frac{5 y}{e ^{2 y}} d y

\frac{d}{d x} (ln (x^{2} + y^{2}))

\frac{\partial}{\partial x} (x^{2} e^{x^{2}})

\frac{\partial}{\partial x} (e^{x} sin (x y))

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