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

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

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integral of sqrt(x-4)

\int x - 4 d x

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

Solution steps

\int x - 4 d x

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

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

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

Substitute back

u = x - 4

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

Add a constant to the solution

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

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

\frac{d}{d x} (\frac{1}{9 + x ^{2}})

\frac{d}{d x} (x y e^{x y})

\frac{\partial}{\partial x} (5 y - x^{3} y^{2})

\frac{d}{d x} (5 x^{2} sin (x) - x)

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