What is the integral of 3/(sqrt(4-5x)) ?

The integral of 3/(sqrt(4-5x)) is -6/5 sqrt(4-5x)+C

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integral of 3/(sqrt(4-5x))

\int \frac{3}{4 - 5 x} d x

- \frac{6}{5} 4 - 5 x + C

Solution steps

\int \frac{3}{4 - 5 x} d x

Take the constant out:

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

= 3 \cdot \int \frac{1}{4 - 5 x} d x

Apply u-substitution

= 3 \cdot \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

= 3 (- \frac{1}{5} \cdot \int \frac{1}{u} d u)

Apply the Power Rule

= 3 (- \frac{1}{5} \cdot 2 u^{\frac{1}{2}})

Substitute back

u = 4 - 5 x

= 3 (- \frac{1}{5} \cdot 2 (4 - 5 x)^{\frac{1}{2}})

Simplify

3 (- \frac{1}{5} \cdot 2 (4 - 5 x)^{\frac{1}{2}}) : - \frac{6}{5} 4 - 5 x

= - \frac{6}{5} 4 - 5 x

Add a constant to the solution

= - \frac{6}{5} 4 - 5 x + C

What is the integral of 3/(sqrt(4-5x)) ?
The integral of 3/(sqrt(4-5x)) is -6/5 sqrt(4-5x)+C