What is the integral of 1/(sqrt(2-x)) ?

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

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integral of 1/(sqrt(2-x))

\int \frac{1}{2 - x} d x

- 2 2 - x + C

Solution steps

\int \frac{1}{2 - x} d x

Apply u-substitution

: \int - \frac{1}{u} d u

= \int - \frac{1}{u} d u

Take the constant out:

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

= - \int \frac{1}{u} d u

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= - 2 u^{\frac{1}{2}}

Substitute back

u = 2 - x

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

Apply radical rule:

= - 2 2 - x

Add a constant to the solution

= - 2 2 - x + C

\frac{5 + x}{1 - 5 x}

x \to 0 lim (\frac{e ^{- 3 x} - 1}{x})

x \to - 4 lim (x^{2} + 4 x)

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (1) = 0

\int sin^{2} (x) \cdot cos (x) d x

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