What is the integral of 4sqrt(t) ?

The integral of 4sqrt(t) is 8/3 t^{3/2}+C

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integral of 4sqrt(t)

\int 4 t d t

\frac{8}{3} t^{\frac{3}{2}} + C

Solution steps

\int 4 t d t

Take the constant out:

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

= 4 \cdot \int t d t

Apply the Power Rule

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

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

Simplify

4 \cdot \frac{2}{3} t^{\frac{3}{2}} : \frac{8}{3} t^{\frac{3}{2}}

= \frac{8}{3} t^{\frac{3}{2}}

Add a constant to the solution

= \frac{8}{3} t^{\frac{3}{2}} + C

\frac{12 s + 5}{s ( s + 3 )}

\frac{\partial}{\partial x} (x (1 - x))

x \to π lim (tan (\frac{x}{3}))

\int_{0}^{2} \frac{x}{1 + x ^{2}} d x

x \to 9 lim (\frac{x - 3}{x - 9})