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

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

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integral of (sin(sqrt(x-2)))/(sqrt(x-2))

\int \frac{sin ( x - 2 )}{x - 2} d x

- 2 cos (x - 2) + C

Solution steps

\int \frac{sin ( x - 2 )}{x - 2} d x

Apply u-substitution

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

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

Apply u-substitution

: \int 2 sin (v) d v

= \int 2 sin (v) d v

Take the constant out:

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

= 2 \cdot \int sin (v) d v

Use the common integral:

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

= 2 (- cos (v))

Substitute back

= 2 (- cos (x - 2))

Simplify

= - 2 cos (x - 2)

Add a constant to the solution

= - 2 cos (x - 2) + C

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