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

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

Popular >

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

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

- 2 a - x + C

Solution steps

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

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

Apply radical rule:

a^{\frac{1}{n}} = n a

= - 2 a - x

Add a constant to the solution

= - 2 a - x + C

\int (- 16 tan (x) cos (x)) d x

\int \frac{e ^{- 2 x}}{x ^{2} e ^{- 2 x}} d x

\int \frac{1 + x ^{4}}{x ^{3} + x} d x

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

\int \frac{x ^{3} + 2 x ^{2} + 5 x + 3}{x ^{2} + x + 2} d x

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