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

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

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integral of sqrt(2x-2)

\int 2 x - 2 d x

\frac{1}{3} (2 x - 2)^{\frac{3}{2}} + C

Solution steps

\int 2 x - 2 d x

Apply u-substitution

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

= \int \frac{u}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int u d u

Apply the Power Rule

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

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

Substitute back

u = 2 x - 2

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

Simplify

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

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

Add a constant to the solution

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

\int x - 2 y + 2

x \to \infty lim (- 2 + x)

\frac{\partial}{\partial x} (\frac{6 x - 9 y}{6 x + 9 y})

y^{^{'}} = - 0.000631594 \cdot y, y (0) = 30

n = 1 \sum \infty \frac{n}{n ^{2} + 25}

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