What is the integral of csc^4(3/2)θ ?

The integral of csc^4(3/2)θ is (csc^4(3/2)θ^2)/2+C

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integral of csc^4(3/2)θ

\int csc^{4} (\frac{3}{2}) θ d θ

\frac{csc ^{4} ( \frac{3}{2} ) θ ^{2}}{2} + C

Solution steps

\int csc^{4} (\frac{3}{2}) θ d θ

Take the constant out:

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

= csc^{4} (\frac{3}{2}) \cdot \int θ d θ

Apply the Power Rule

: \frac{θ ^{2}}{2}

= csc^{4} (\frac{3}{2}) \frac{θ ^{2}}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{csc ^{4} ( \frac{3}{2} ) θ ^{2}}{2}

Add a constant to the solution

= \frac{csc ^{4} ( \frac{3}{2} ) θ ^{2}}{2} + C

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What is the integral of csc^4(3/2)θ ?
The integral of csc^4(3/2)θ is (csc^4(3/2)θ^2)/2+C