What is the integral of 1.5sqrt(x) ?

The integral of 1.5sqrt(x) is x^{3/2}+C

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integral of 1.5sqrt(x)

\int 1.5 x d x

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

Solution steps

\int 1.5 x d x

Take the constant out:

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

= 1.5 \cdot \int x d x

Apply the Power Rule

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

= 1.5 \cdot \frac{2}{3} x^{\frac{3}{2}}

Simplify

1.5 \cdot \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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