What is the integral of (cos(sqrt(1-x)))/(sqrt(1-x)) ?

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

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integral of (cos(sqrt(1-x)))/(sqrt(1-x))

\int \frac{cos ( 1 - x )}{1 - x} d x

- 2 sin (1 - x) + C

Solution steps

\int \frac{cos ( 1 - x )}{1 - x} d x

Apply u-substitution

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

Take the constant out:

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

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

Apply u-substitution

= - \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 (1 - x)

Add a constant to the solution

= - 2 sin (1 - x) + C

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