What is the integral of sqrt(3t) ?

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

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integral of sqrt(3t)

\int 3 t d t

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

Solution steps

\int 3 t d t

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \int 3 t d t

Take the constant out:

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

= 3 \cdot \int t d t

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

e^{- 2 t} \cdot (t^{2} + 4 t + 5)

\frac{\partial}{\partial x} \frac{1}{f ( x ) ^{^{'}} ( f ( x ) ^{- 1} ( x ) )}

\frac{\partial}{\partial x} (\frac{y}{2 x} - 1)

\frac{\partial}{\partial x} (2 π \frac{x}{y})

2 y d x = 3 x d y

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