What is the integral of (3sqrt(x))/4 ?

The integral of (3sqrt(x))/4 is 1/2 x^{3/2}+C

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integral of (3sqrt(x))/4

\int \frac{3 x}{4} d x

\frac{1}{2} x^{\frac{3}{2}} + C

Solution steps

\int \frac{3 x}{4} d x

Take the constant out:

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

= \frac{3}{4} \cdot \int x d x

Apply the Power Rule

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

= \frac{3}{4} \cdot \frac{2}{3} x^{\frac{3}{2}}

Simplify

\frac{3}{4} \cdot \frac{2}{3} x^{\frac{3}{2}} : \frac{1}{2} x^{\frac{3}{2}}

= \frac{1}{2} x^{\frac{3}{2}}

Add a constant to the solution

= \frac{1}{2} x^{\frac{3}{2}} + C

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What is the integral of (3sqrt(x))/4 ?
The integral of (3sqrt(x))/4 is 1/2 x^{3/2}+C