What is the integral of 3/(sqrt(1-2x)) ?

The integral of 3/(sqrt(1-2x)) is -3sqrt(1-2x)+C

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integral of 3/(sqrt(1-2x))

\int \frac{3}{1 - 2 x} d x

- 3 1 - 2 x + C

Solution steps

\int \frac{3}{1 - 2 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}{1 - 2 x} d x

Apply u-substitution

= 3 \cdot \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

= 3 (- \frac{1}{2} \cdot \int \frac{1}{u} d u)

Apply the Power Rule

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

Substitute back

u = 1 - 2 x

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

Simplify

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

= - 3 1 - 2 x

Add a constant to the solution

= - 3 1 - 2 x + C

What is the integral of 3/(sqrt(1-2x)) ?
The integral of 3/(sqrt(1-2x)) is -3sqrt(1-2x)+C