What is the integral of sin(1/10)xsin(1/20)x ?

The integral of sin(1/10)xsin(1/20)x is 1/3 sin(1/10)sin(1/20)x^3+C

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integral of sin(1/10)xsin(1/20)x

\int sin (\frac{1}{10}) x sin (\frac{1}{20}) x d x

\frac{1}{3} sin (\frac{1}{10}) sin (\frac{1}{20}) x^{3} + C

Solution steps

\int sin (\frac{1}{10}) x sin (\frac{1}{20}) x d x

Take the constant out:

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

= sin (\frac{1}{10}) sin (\frac{1}{20}) \cdot \int xx d x

Simplify

xx : x^{2}

= sin (\frac{1}{10}) sin (\frac{1}{20}) \cdot \int x^{2} d x

Apply the Power Rule

= sin (\frac{1}{10}) sin (\frac{1}{20}) \frac{x ^{3}}{3}

Simplify

sin (\frac{1}{10}) sin (\frac{1}{20}) \frac{x ^{3}}{3} : \frac{1}{3} sin (\frac{1}{10}) sin (\frac{1}{20}) x^{3}

= \frac{1}{3} sin (\frac{1}{10}) sin (\frac{1}{20}) x^{3}

Add a constant to the solution

= \frac{1}{3} sin (\frac{1}{10}) sin (\frac{1}{20}) x^{3} + C

What is the integral of sin(1/10)xsin(1/20)x ?
The integral of sin(1/10)xsin(1/20)x is 1/3 sin(1/10)sin(1/20)x^3+C