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

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

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

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

3 2 x - 1 + C

Solution steps

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

Apply the Power Rule

= 3 \cdot \frac{1}{2} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 2 x - 1

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

Simplify

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

= 3 2 x - 1

Add a constant to the solution

= 3 2 x - 1 + C

d y - k y d x = 0

\int \frac{1}{4 u ^{2} + 23} d u

t an g e n t f (x) = x^{2} + 9, (- 5, 34)

\int 1 - e^{2 x} d x

x \to 0 lim (\frac{3}{x} - \frac{2}{ln ( x )})

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