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

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

Popular >

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

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

- \frac{2}{5} 1 - 5 x + C

Solution steps

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

Apply u-substitution

: \int - \frac{1}{5 u} d u

= \int - \frac{1}{5 u} d u

Take the constant out:

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

= - \frac{1}{5} \cdot \int \frac{1}{u} d u

Apply the Power Rule

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

= - \frac{1}{5} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 1 - 5 x

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

Simplify

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

= - \frac{2}{5} 1 - 5 x

Add a constant to the solution

= - \frac{2}{5} 1 - 5 x + C

\int \frac{35}{1 + 25 x ^{2}} d x

\int \frac{1}{s ^{3}} d s

\int - 16 - x^{2} d x

\int (\frac{ln ( x ^{6} )}{x}) d x

\int (x^{2} + 4 x + 3) d x

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