What is the integral of sin(2x-3) ?

The integral of sin(2x-3) is -1/2 cos(2x-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(2x-3)

\int sin (2 x - 3) d x

- \frac{1}{2} cos (2 x - 3) + C

Solution steps

\int sin (2 x - 3) d x

Apply u-substitution

: \int sin (u) \frac{1}{2} d u

= \int sin (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 sin (u) d u

Use the common integral:

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

= \frac{1}{2} (- cos (u))

Substitute back

u = 2 x - 3

= \frac{1}{2} (- cos (2 x - 3))

Simplify

= - \frac{1}{2} cos (2 x - 3)

Add a constant to the solution

= - \frac{1}{2} cos (2 x - 3) + C

\int x^{4} (ln (x) - 2) d x

\int \frac{x ^{4}}{( 1 + x ^{2} ) ^{2}} d x

\int x tan (x^{2}) sec (x^{2}) d x

\int \frac{y}{8 - y} d y

\int \frac{x ^{2} + 2}{x ^{2} - 4} - x d x

What is the integral of sin(2x-3) ?
The integral of sin(2x-3) is -1/2 cos(2x-3)+C