What is the integral of 1/(sqrt(5-x)) ?

The integral of 1/(sqrt(5-x)) is -2sqrt(5-x)+C

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integral of 1/(sqrt(5-x))

\int \frac{1}{5 - x} d x

- 2 5 - x + C

Solution steps

\int \frac{1}{5 - 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 = 5 - x

= - 2 (5 - x)^{\frac{1}{2}}

Apply radical rule:

= - 2 5 - x

Add a constant to the solution

= - 2 5 - x + C

\int 256 - x^{2} d x

\int \frac{2 x}{2 x ^{2} + 1} d x

\frac{d y}{d x} = \frac{3 x ^{2}}{e ^{2 y}}, y (0) = \frac{1}{2}

2 x (x^{2} - 4 x + 5)^{8}, at x = 2

y^{^{''}} + 3 y^{^{'}} + 2 y = 12 t^{3}

What is the integral of 1/(sqrt(5-x)) ?
The integral of 1/(sqrt(5-x)) is -2sqrt(5-x)+C