What is the integral of sqrt(4x) ?

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

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integral of sqrt(4x)

\int 4 x d x

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

Solution steps

\int 4 x d x

Simplify

4 x : 2 x

= \int 2 x d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d 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 (\frac{6 sin ( x )}{x})

\int_{1}^{\infty} \frac{2}{e ^{x}} d x

\frac{\partial}{\partial x} (6 y^{2} - 6 x^{2})

f (x) = x^{2} + 2, (2, 6)

f (x) = x^{2} - x, at x = 4