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

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

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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

: \int \frac{1}{2 u} d u

= 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

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

= 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

y^{^{'}} - 1 0^{- 3} y = 220 cos (50 x)

d y - k y d x = 0

x \to 1 lim (\frac{2 x + 1}{x - 1})

n = 7 \sum \infty (\frac{6}{7})^{- n}

y = x^{6}

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