What is the integral of 2sqrt(t) ?

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

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integral of 2sqrt(t)

\int 2 t d t

\frac{4}{3} t^{\frac{3}{2}} + C

Solution steps

\int 2 t d t

Take the constant out:

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

= 2 \cdot \int t d t

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

= \frac{4}{3} t^{\frac{3}{2}} + C

\frac{d}{d x} (\frac{x ^{2} - 1}{x + 2})

\frac{d y}{d x} = x y + x + y + 1

\frac{\partial}{\partial y} (x^{2} \cdot y^{3})

\frac{4 x ^{3} + 2 x + 5}{x}

x \to 0 lim (\frac{5 ^{x} - 3 ^{x}}{x})