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

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

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integral of 2sqrt(a)sqrt(x)

\int 2 a x d x

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

Solution steps

\int 2 a x d x

Take the constant out:

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

= 2 a \cdot \int x d x

Apply the Power Rule

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

Simplify

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

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

Add a constant to the solution

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

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

\frac{\partial}{\partial x} (\frac{( 3 x - y )}{( x + 2 y )})

\int \frac{7 x ^{2} + 2 x - 7}{x ^{3} - x} d x

\frac{d y}{d x} + y = y^{2}

\int x \cdot e^{1 - x^{2}} d x

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