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

The integral of sqrt(3x-4) is 2/9 (3x-4)^{3/2}+C

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integral of sqrt(3x-4)

\int 3 x - 4 d x

\frac{2}{9} (3 x - 4)^{\frac{3}{2}} + C

Solution steps

\int 3 x - 4 d x

Apply u-substitution

: \int \frac{u}{3} d u

= \int \frac{u}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int u d u

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

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

Substitute back

u = 3 x - 4

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

Simplify

\frac{1}{3} \cdot \frac{2}{3} (3 x - 4)^{\frac{3}{2}} : \frac{2}{9} (3 x - 4)^{\frac{3}{2}}

= \frac{2}{9} (3 x - 4)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{9} (3 x - 4)^{\frac{3}{2}} + C

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

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

\frac{d y}{d x} = \frac{1}{x}

\int_{0}^{1} (e^{x^{2}}) d x

\frac{x}{y} \frac{d y}{d x} + ln (y) = x + 1

What is the integral of sqrt(3x-4) ?
The integral of sqrt(3x-4) is 2/9 (3x-4)^{3/2}+C