What is the integral of sin^4(1/2)x ?

The integral of sin^4(1/2)x is (sin^4(1/2)x^2)/2+C

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integral of sin^4(1/2)x

\int sin^{4} (\frac{1}{2}) x d x

\frac{sin ^{4} ( \frac{1}{2} ) x ^{2}}{2} + C

Solution steps

\int sin^{4} (\frac{1}{2}) x d x

Take the constant out:

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

= sin^{4} (\frac{1}{2}) \cdot \int x d x

Apply the Power Rule

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

= sin^{4} (\frac{1}{2}) \frac{x ^{2}}{2}

Multiply fractions:

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

= \frac{sin ^{4} ( \frac{1}{2} ) x ^{2}}{2}

Add a constant to the solution

= \frac{sin ^{4} ( \frac{1}{2} ) x ^{2}}{2} + C

\int (3 x + 15) x^{2} + 10 x + 4 d x

\int (e^{2 t}) d t

\frac{sin ( 3 x )}{tan ( 4 x )}

\frac{1}{x - 1}, 21

f (x) = e^{x} (tan (x) - x)

What is the integral of sin^4(1/2)x ?
The integral of sin^4(1/2)x is (sin^4(1/2)x^2)/2+C