What is the integral of sqrt((5x)/8) ?

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

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integral of sqrt((5x)/8)

\int \frac{5 x}{8} d x

\frac{5}{3 2} x^{\frac{3}{2}} + C

Solution steps

\int \frac{5 x}{8} d x

Simplify

\frac{5 x}{8} : \frac{5}{2 2} x

= \int \frac{5}{2 2} x d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{5}{2 2} \cdot \int x d x

Apply the Power Rule

: \frac{2}{3} x^{\frac{3}{2}}

= \frac{5}{2 2} \cdot \frac{2}{3} x^{\frac{3}{2}}

Simplify

\frac{5}{2 2} \cdot \frac{2}{3} x^{\frac{3}{2}} : \frac{5}{3 2} x^{\frac{3}{2}}

= \frac{5}{3 2} x^{\frac{3}{2}}

Add a constant to the solution

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

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

\int (16 x + 5) 8 x^{2} + 5 x d x

\int x d (arcsin (x)) d x

\int x sin (\frac{x}{5}) d x

\int (3 x^{2} + 5 x) d x

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