What is the integral of-(cos(nx))/n ?

The integral of-(cos(nx))/n is -1/(n^2)sin(nx)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of-(cos(nx))/n

\int - \frac{cos ( n x )}{n} d x

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

Solution steps

\int - \frac{cos ( n x )}{n} d x

Take the constant out:

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

= - \frac{1}{n} \cdot \int cos (n x) d x

Apply u-substitution

: \int \frac{cos ( u )}{n} d u

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

Take the constant out:

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

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

Use the common integral:

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

= - \frac{1}{n} \cdot \frac{1}{n} sin (u)

Substitute back

u = n x

= - \frac{1}{n} \cdot \frac{1}{n} sin (n x)

Simplify

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

= - \frac{1}{n ^{2}} sin (n x)

Add a constant to the solution

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

\int (π t - t^{2}) cos (n t) d t

\int - 3 cos (t) d t

y^{^{''}} - 2 y^{^{'}} + 5 y = 2 cos (2 t) e^{t}

y = \frac{2 x}{3 - cot ( x )}

(e)^{^{'}}

What is the integral of-(cos(nx))/n ?
The integral of-(cos(nx))/n is -1/(n^2)sin(nx)+C