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

The integral of sin(2/3)x is 1/2 sin(2/3)x^2+C

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integral of sin(2/3)x

\int sin (\frac{2}{3}) x d x

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

Solution steps

\int sin (\frac{2}{3}) x d x

Take the constant out:

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

= sin (\frac{2}{3}) \cdot \int x d x

Apply the Power Rule

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

= sin (\frac{2}{3}) \frac{x ^{2}}{2}

Simplify

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

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

Add a constant to the solution

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

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