What is the integral of (3x)/(2sqrt(x)) ?

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

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integral of (3x)/(2sqrt(x))

\int \frac{3 x}{2 x} d x

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

Solution steps

\int \frac{3 x}{2 x} d x

Take the constant out:

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

= \frac{3}{2} \cdot \int \frac{x}{x} d x

Simplify

\frac{x}{x} : x

= \frac{3}{2} \cdot \int x d x

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

x \to 4 + lim (\frac{6 x}{x - 4})

f (x) = ln (x^{8})

\frac{d}{d y} (arctan (x y))

\int - 15 d x

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