What is the integral of (x-8)^{3/2} ?

The integral of (x-8)^{3/2} is 2/5 (x-8)^{5/2}+C

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integral of (x-8)^{3/2}

\int (x - 8)^{\frac{3}{2}} d x

\frac{2}{5} (x - 8)^{\frac{5}{2}} + C

Solution steps

\int (x - 8)^{\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 - 8

= \frac{2}{5} (x - 8)^{\frac{5}{2}}

Add a constant to the solution

= \frac{2}{5} (x - 8)^{\frac{5}{2}} + C

\frac{d}{d x} (e^{2 x y})

f (x) = x^{2} (1 - 4 x)

f (x) = x^{3} - 6 x^{2} - 34 x + 40, at x = - 3

\int_{0}^{7} x 49 - x^{2} d x

\int_{0}^{2} x (x^{2} - 1)^{3} d x

What is the integral of (x-8)^{3/2} ?
The integral of (x-8)^{3/2} is 2/5 (x-8)^{5/2}+C