What is the integral of 5sqrt(t^3) ?

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

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integral of 5sqrt(t^3)

\int 5 t^{3} d t

2 t^{\frac{5}{2}} + C

Solution steps

\int 5 t^{3} d t

Take the constant out:

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

= 5 \cdot \int t^{3} d t

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

assuming

t \geq 0

= 5 \cdot \int t^{\frac{3}{2}} d t

Apply the Power Rule

: \frac{2}{5} t^{\frac{5}{2}}

= 5 \cdot \frac{2}{5} t^{\frac{5}{2}}

Simplify

5 \cdot \frac{2}{5} t^{\frac{5}{2}} : 2 t^{\frac{5}{2}}

= 2 t^{\frac{5}{2}}

Add a constant to the solution

= 2 t^{\frac{5}{2}} + C

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