What is the integral of (2x)^{1/2} ?

The integral of (2x)^{1/2} is 2^{1/2}*2/3 x^{3/2}+C

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integral of (2x)^{1/2}

\int (2 x)^{\frac{1}{2}} d x

2^{\frac{1}{2}} \cdot \frac{2}{3} x^{\frac{3}{2}} + C

Solution steps

\int (2 x)^{\frac{1}{2}} d x

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

= \int 2^{\frac{1}{2}} x^{\frac{1}{2}} d x

Take the constant out:

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

= 2^{\frac{1}{2}} \cdot \int x^{\frac{1}{2}} d x

Apply the Power Rule

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

= 2^{\frac{1}{2}} \cdot \frac{2}{3} x^{\frac{3}{2}}

Add a constant to the solution

= 2^{\frac{1}{2}} \cdot \frac{2}{3} x^{\frac{3}{2}} + C

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

\int \frac{1}{cot ( 3 x )} d x

y^{^{'}} = \frac{x ^{2} + 3}{y}, y (0) = 1

x e^{x}

x \to - 4 lim (16 - x^{2})

What is the integral of (2x)^{1/2} ?
The integral of (2x)^{1/2} is 2^{1/2}*2/3 x^{3/2}+C