What is the integral of (2x)/(sqrt(x)) ?

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

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integral of (2x)/(sqrt(x))

\int \frac{2 x}{x} d x

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

Solution steps

\int \frac{2 x}{x} d x

Take the constant out:

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

= 2 \cdot \int \frac{x}{x} d x

Simplify

\frac{x}{x} : x

= 2 \cdot \int x d x

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

x \to 0 lim (+ (e^{x}))

\int (3 x + 1)^{2} d x

e^{- 0.5 x}

\frac{d}{d t} ((A t^{2} + Bt + C) (sin (2 t) + cos (2 t)))

x \to \infty lim (\frac{x}{r})

What is the integral of (2x)/(sqrt(x)) ?
The integral of (2x)/(sqrt(x)) is 4/3 x^{3/2}+C