What is the integral of sqrt((5x)/4) ?

The integral of sqrt((5x)/4) is (sqrt(5))/3 x^{3/2}+C

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integral of sqrt((5x)/4)

\int \frac{5 x}{4} d x

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

Solution steps

\int \frac{5 x}{4} d x

Simplify

\frac{5 x}{4} : \frac{5}{2} x

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

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

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What is the integral of sqrt((5x)/4) ?
The integral of sqrt((5x)/4) is (sqrt(5))/3 x^{3/2}+C