What is the integral of 1.5sqrt(t) ?

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

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integral of 1.5sqrt(t)

\int 1.5 t d t

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

Solution steps

\int 1.5 t d t

Take the constant out:

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

= 1.5 \cdot \int t d t

Apply the Power Rule

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

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

Simplify

1.5 \cdot \frac{2}{3} t^{\frac{3}{2}} : t^{\frac{3}{2}}

= t^{\frac{3}{2}}

Add a constant to the solution

= t^{\frac{3}{2}} + C

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