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

The integral of cos(2*x) is 1/2 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 cos(2*x)

\int cos (2 \cdot x) d 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

\int sin (tan (x)) d x

\int \frac{x + 1}{x - 1} d x

\int 2 x + 4 y d x

\int e^{e^{e^{x}}} d e^{e^{x}}

\int \frac{1}{2 + cos ^{2} ( x )} d x