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

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

Popular >

integral of cos(2x)2

\int cos (2 x) 2 d x

sin (2 x) + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

= 2 \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

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

Use the common integral:

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

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

Substitute back

u = 2 x

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

Simplify

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

= sin (2 x)

Add a constant to the solution

= sin (2 x) + C

x \to - 5 + lim (\frac{x - 5}{x + 5})

\frac{d x}{d t} = 375 - \frac{3 x}{800 + 2 t}

\frac{x ^{4}}{12}

y^{^{'}} = \frac{( y ^{2} + x y - x ^{2} )}{x ^{2}}

\frac{1}{3 x + 2}