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

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

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integral of sqrt(x-a)

\int x - a d x

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

Solution steps

\int x - a d x

Apply u-substitution

= \int u d u

Apply the Power Rule

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

Substitute back

u = x - a

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

Add a constant to the solution

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

\int \frac{u}{u} d u

\int (x^{\frac{3}{2}} + 3)^{4} x d x

\int x^{3} 1 + 3 x^{2} d x

\int \frac{x ^{2} - 6}{x ^{2} - 9} d x

\int t^{\frac{7}{2}} (t^{2} - 10 t + 17) d t

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