What is the integral of cos(2x) ?

The integral of cos(2x) is 1/2 sin(2x)+C

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integral of cos(2x)

integral

cos (2 x)

\frac{1}{2} sin (2 x) + C

Solution steps

\int cos (2 x) d x

Apply u-substitution

: \int cos (u) \frac{1}{2} d u

= \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

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

Use the common integral:

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

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

Substitute back

u = 2 x

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

Add a constant to the solution

= \frac{1}{2} sin (2 x) + C

(- 1.5) (5.5)

f (x) = \frac{1}{4} x^{8} - \frac{1}{2} x^{6} - x + 2

y = \frac{4}{x}

x = 6

f (x) = 4 e^{x} cos (x)