What is the integral of cos(2x)16 ?

The integral of cos(2x)16 is 8sin(2x)+C

integral of cos(2x)16

\int cos (2 x) 16 d x

8 sin (2 x) + C

Solution steps

\int cos (2 x) \cdot 16 d x

Take the constant out:

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

= 16 \cdot \int cos (2 x) d x

Apply u-substitution

= 16 \cdot \int cos (u) \frac{1}{2} d u

Take the constant out:

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

= 16 \cdot \frac{1}{2} \cdot \int cos (u) d u

Use the common integral:

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

= 16 \cdot \frac{1}{2} sin (u)

Substitute back

u = 2 x

= 16 \cdot \frac{1}{2} sin (2 x)

Simplify

16 \cdot \frac{1}{2} sin (2 x) : 8 sin (2 x)

= 8 sin (2 x)

Add a constant to the solution

= 8 sin (2 x) + C

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