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

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

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integral of cos(sqrt(1-x))

\int cos (1 - x) d x

- 2 (sin (1 - x) 1 - x + cos (1 - x)) + C

Solution steps

\int cos (1 - x) d x

Apply u-substitution

: \int - cos (u) d u

= \int - cos (u) d u

Take the constant out:

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

= - \int cos (u) d u

Apply u-substitution

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

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

Apply Integration By Parts

: v sin (v) - \int sin (v) d v

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

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

= - 2 (v sin (v) - (- cos (v)))

Substitute back

= - 2 (1 - x sin (1 - x) - (- cos (1 - x)))

Simplify

= - 2 (sin (1 - x) 1 - x + cos (1 - x))

Add a constant to the solution

= - 2 (sin (1 - x) 1 - x + cos (1 - x)) + C

\frac{d}{d x} (\frac{2}{( 1 - x ) ^{2}})

\int \frac{x ^{3} - 2}{x ^{2} + 3 x + 2} d x

\frac{d}{d x} (\frac{1}{x ^{3} - 2 x})

n \to \infty lim (- 1^{n})

\int_{0}^{π} 4 sin (x) + sin (4 x) d x

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