What is the integral of (10)/(sqrt(5-x)) ?

The integral of (10)/(sqrt(5-x)) is -20sqrt(5-x)+C

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integral of (10)/(sqrt(5-x))

\int \frac{10}{5 - x} d x

- 20 5 - x + C

Solution steps

\int \frac{10}{5 - x} d x

Take the constant out:

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

= 10 \cdot \int \frac{1}{5 - x} d x

Apply u-substitution

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

= 10 \cdot \int - \frac{1}{u} d u

Take the constant out:

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

= 10 (- \int \frac{1}{u} d u)

Apply the Power Rule

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

= 10 (- 2 u^{\frac{1}{2}})

Substitute back

u = 5 - x

= 10 (- 2 (5 - x)^{\frac{1}{2}})

Simplify

10 (- 2 (5 - x)^{\frac{1}{2}}) : - 20 5 - x

= - 20 5 - x

Add a constant to the solution

= - 20 5 - x + C

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

\frac{\partial}{\partial x} (x^{2} + x y + 5 y)

x \to 2 lim (6 x^{2})

\frac{d}{d x} (\frac{x ^{2} + x}{2 x + 5})

x \to - \infty lim (\frac{x}{- x})

What is the integral of (10)/(sqrt(5-x)) ?
The integral of (10)/(sqrt(5-x)) is -20sqrt(5-x)+C