What is the integral of (x-2)^{3/2} ?

The integral of (x-2)^{3/2} is 2/5 (x-2)^{5/2}+C

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integral of (x-2)^{3/2}

\int (x - 2)^{\frac{3}{2}} d x

\frac{2}{5} (x - 2)^{\frac{5}{2}} + C

Solution steps

\int (x - 2)^{\frac{3}{2}} d x

Apply u-substitution

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

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

Apply the Power Rule

: \frac{2}{5} u^{\frac{5}{2}}

= \frac{2}{5} u^{\frac{5}{2}}

Substitute back

u = x - 2

= \frac{2}{5} (x - 2)^{\frac{5}{2}}

Add a constant to the solution

= \frac{2}{5} (x - 2)^{\frac{5}{2}} + C

x \to 7 - lim (\frac{2 x + 1}{x - 7})

x \to \infty lim (1.0 7^{x})

3 sin (t) - 3 cos (t)

f (x) = \frac{4 + x}{x - 2}, at x = 8

x y y^{^{'}} = x^{2} + 3 y^{2}

What is the integral of (x-2)^{3/2} ?
The integral of (x-2)^{3/2} is 2/5 (x-2)^{5/2}+C