What is the integral of sin(2x-5) ?

The integral of sin(2x-5) is -1/2 cos(2x-5)+C

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integral of sin(2x-5)

\int sin (2 x - 5) d x

- \frac{1}{2} cos (2 x - 5) + C

Solution steps

\int sin (2 x - 5) 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 - 5

= \frac{1}{2} (- cos (2 x - 5))

Simplify

= - \frac{1}{2} cos (2 x - 5)

Add a constant to the solution

= - \frac{1}{2} cos (2 x - 5) + C

\int_{0}^{2 π} 7 x^{2} sin (\frac{1}{4} x) d x

\frac{d y}{d x} = \frac{( y - x )}{x}

n = 2 \sum \infty - \frac{1}{4 ^{n}}

x \to 0 lim (\frac{9 ^{x} - 5 ^{x}}{x})

\frac{\partial}{\partial y} (\frac{y ln ( y )}{x - 1})

What is the integral of sin(2x-5) ?
The integral of sin(2x-5) is -1/2 cos(2x-5)+C