What is the integral of sin(xn) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(xn)

\int sin (x n) d x

- \frac{1}{n} cos (n x) + C

Solution steps

\int sin (x n) d x

Apply u-substitution

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

= \int \frac{sin ( 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 \int sin (u) d u

Use the common integral:

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

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

Substitute back

u = x n

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

Simplify

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

Add a constant to the solution

= - \frac{1}{n} cos (n x) + C

\frac{d P}{d t} = \frac{9 P}{900} (9 - P), P (0) = 4

- 12 sin (2 x)

\int x^{3} \cdot 9 - x^{2} d x

\frac{d}{d x} ((\frac{3 x}{x + 1})^{2})

2 x^{3}