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

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

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integral of sqrt(x/a)

\int \frac{x}{a} d x

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

Solution steps

\int \frac{x}{a} d x

Apply Integration By Parts

= \frac{x}{a} x - \int \frac{x}{2 a} d x

\int \frac{x}{2 a} d x = \frac{x ^{\frac{3}{2}}}{3 a}

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

Add a constant to the solution

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

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