What is the integral of cos(0.5x) ?

The integral of cos(0.5x) is 2sin(0.5x)+C

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integral of cos(0.5x)

\int cos (0.5 x) d x

2 sin (0.5 x) + C

Solution steps

\int cos (0.5 x) d x

Apply u-substitution

= \int cos (u) \frac{1}{0.5} d u

Take the constant out:

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

= \frac{1}{0.5} \cdot \int cos (u) d u

Simplify

= 2 \cdot \int cos (u) d u

Use the common integral:

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

= 2 sin (u)

Substitute back

u = 0.5 x

= 2 sin (0.5 x)

Add a constant to the solution

= 2 sin (0.5 x) + C