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

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

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

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

2 sin (x - 2) + C

Solution steps

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

Apply u-substitution

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

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

Apply u-substitution

: \int 2 cos (v) d v

= \int 2 cos (v) d v

Take the constant out:

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

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

Use the common integral:

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

= 2 sin (v)

Substitute back

= 2 sin (x - 2)

Add a constant to the solution

= 2 sin (x - 2) + C

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\int \frac{2 x - 13}{x ^{2} - 8 x + 16} d x

\int \frac{200}{( x + 2 ) ^{2}} d x

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