What is the integral of sqrt(x-5) ?

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

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integral of sqrt(x-5)

\int x - 5 d x

\frac{2}{3} (x - 5)^{\frac{3}{2}} + C

Solution steps

\int x - 5 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 - 5

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

Add a constant to the solution

= \frac{2}{3} (x - 5)^{\frac{3}{2}} + C

\int \frac{17}{( x ^{2} - 1 ) ^{2}} d x

x \to 1 lim ((1 - \frac{5}{x})^{x})

(8 x + 5) (x^{2} - 3 x)

{(cos (3 t) - 9)^{2}}

y^{^{'}} + \frac{1}{20} y = 0

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