What is the integral of sin(5x-3) ?

The integral of sin(5x-3) is -1/5 cos(5x-3)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(5x-3)

\int sin (5 x - 3) d x

- \frac{1}{5} cos (5 x - 3) + C

Solution steps

\int sin (5 x - 3) d x

Apply u-substitution

: \int sin (u) \frac{1}{5} d u

= \int sin (u) \frac{1}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{5} (- cos (u))

Substitute back

u = 5 x - 3

= \frac{1}{5} (- cos (5 x - 3))

Simplify

= - \frac{1}{5} cos (5 x - 3)

Add a constant to the solution

= - \frac{1}{5} cos (5 x - 3) + C

f (x) = (x^{2}) sin (x - 2)

\frac{d}{d x} (e^{x} (x - 1) (x^{2} - 1))

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

\int_{- 1}^{1} (y^{2} - 2) - e^{y} d y

\frac{e ^{x^{2}} - 1}{x}

What is the integral of sin(5x-3) ?
The integral of sin(5x-3) is -1/5 cos(5x-3)+C