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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2cos(2x)

\int 2 cos (2 x) d x

sin (2 x) + C

Solution steps

\int 2 cos (2 x) 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

\int \frac{4 x}{50 - x ^{2}} d x

arctan (x^{2})

\frac{d y}{d x} - \frac{3 x ^{2}}{2 y} = 0

\frac{d}{d x} (arctan (2 x^{4}))

\int (x^{2} + 3)^{4} 2 x d x