What is the integral of 1/3 sin(x) ?

The integral of 1/3 sin(x) is -1/3 cos(x)+C

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integral of 1/3 sin(x)

\int \frac{1}{3} sin (x) d x

- \frac{1}{3} cos (x) + C

Solution steps

\int \frac{1}{3} sin (x) d x

Take the constant out:

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

= \frac{1}{3} \cdot \int sin (x) d x

Use the common integral:

\int sin (x) d x = - cos (x)

= \frac{1}{3} (- cos (x))

Simplify

= - \frac{1}{3} cos (x)

Add a constant to the solution

= - \frac{1}{3} cos (x) + C

\int 21 tan^{3} (θ) d θ

y^{^{'}} - \frac{4}{x} y = 4 x^{5}

\frac{d}{d x} (\frac{x}{csch ( x )})

\int 30 x \cdot (x + 1)^{4} d x

\frac{d}{d x} (\frac{2 x}{( 1 + x ^{2} ) ^{2}})

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