What is the integral of sin^4(2a)x ?

The integral of sin^4(2a)x is (x^2sin^4(2a))/2+C

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integral of sin^4(2a)x

\int sin^{4} (2 a) x d x

\frac{x ^{2} sin ^{4} ( 2 a )}{2} + C

Solution steps

\int sin^{4} (2 a) x d x

Take the constant out:

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

= sin^{4} (2 a) \cdot \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= sin^{4} (2 a) \frac{x ^{2}}{2}

Multiply fractions:

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

= \frac{x ^{2} sin ^{4} ( 2 a )}{2}

Add a constant to the solution

= \frac{x ^{2} sin ^{4} ( 2 a )}{2} + C

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What is the integral of sin^4(2a)x ?
The integral of sin^4(2a)x is (x^2sin^4(2a))/2+C