What is the integral of (3sqrt(x))/(-2) ?

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

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integral of (3sqrt(x))/(-2)

\int \frac{3 x}{- 2} d x

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

Solution steps

\int \frac{3 x}{- 2} d x

Take the constant out:

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

= \frac{3}{- 2} \cdot \int x d x

Simplify

= (- \frac{3}{2}) \cdot \int x d x

Apply the Power Rule

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

Simplify

(- \frac{3}{2}) \frac{2}{3} x^{\frac{3}{2}} : - x^{\frac{3}{2}}

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

Add a constant to the solution

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

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