What is the integral of cos(2npix) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of cos(2npix)

\int cos (2 nπ x) d x

\frac{1}{2 πn} sin (2 nπ x) + C

Solution steps

\int cos (2 nπ x) d x

Apply u-substitution

: \int \frac{cos ( u )}{2 πn} d u

= \int \frac{cos ( u )}{2 πn} d u

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{2 πn} sin (u)

Substitute back

u = 2 nπ x

= \frac{1}{2 πn} sin (2 nπ x)

Add a constant to the solution

= \frac{1}{2 πn} sin (2 nπ x) + C

\int cos^{2} (6 x) sin^{2} (6 x) d x

\int \frac{1}{18 x ^{5}} d x

\int (6 x^{2} - 7 x + 5) d x

\int (2 x + 1) e^{- 3 x} d x

\int \frac{3 x ^{3} + x ^{2} + 5 x + 1}{x ^{3} + x} d x

What is the integral of cos(2npix) ?
The integral of cos(2npix) is 1/(2pin)sin(2npix)+C