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

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

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integral of cos(1/3 x)

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

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

Solution steps

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

Apply u-substitution

= \int cos (u) \cdot 3 d u

Take the constant out:

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

= 3 \cdot \int cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= 3 sin (u)

Substitute back

u = \frac{1}{3} x

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

Add a constant to the solution

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

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