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

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

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integral of 1/(sqrt(5-2x))

\int \frac{1}{5 - 2 x} d x

- 5 - 2 x + C

Solution steps

\int \frac{1}{5 - 2 x} d x

Apply u-substitution

: \int - \frac{1}{2 u} d u

= \int - \frac{1}{2 u} d u

Take the constant out:

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

= - \frac{1}{2} \cdot \int \frac{1}{u} d u

Apply the Power Rule

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

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

Substitute back

u = 5 - 2 x

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

Simplify

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

= - 5 - 2 x

Add a constant to the solution

= - 5 - 2 x + C

t \to 0 lim (sin (7 t))

ln (9 x^{2} + 5 y^{2})

\int 3^{- x} sin (x) d x

y^{3} \cdot \frac{d y}{d x} + x^{3} = 0

(\frac{x ^{2} + 6}{x ^{2} - 6})^{4}

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