What is the integral of sin(3/2)θcos(3/2)θ ?

The integral of sin(3/2)θcos(3/2)θ is 1/3 sin(3/2)cos(3/2)θ^3+C

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integral of sin(3/2)θcos(3/2)θ

\int sin (\frac{3}{2}) θ cos (\frac{3}{2}) θ d θ

\frac{1}{3} sin (\frac{3}{2}) cos (\frac{3}{2}) θ^{3} + C

Solution steps

\int sin (\frac{3}{2}) θ cos (\frac{3}{2}) θ d θ

Take the constant out:

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

= sin (\frac{3}{2}) cos (\frac{3}{2}) \cdot \int θθ d θ

Simplify

θθ : θ^{2}

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

Apply the Power Rule

= sin (\frac{3}{2}) cos (\frac{3}{2}) \frac{θ ^{3}}{3}

Simplify

sin (\frac{3}{2}) cos (\frac{3}{2}) \frac{θ ^{3}}{3} : \frac{1}{3} sin (\frac{3}{2}) cos (\frac{3}{2}) θ^{3}

= \frac{1}{3} sin (\frac{3}{2}) cos (\frac{3}{2}) θ^{3}

Add a constant to the solution

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

What is the integral of sin(3/2)θcos(3/2)θ ?
The integral of sin(3/2)θcos(3/2)θ is 1/3 sin(3/2)cos(3/2)θ^3+C