What is the integral of 2x^{3/2} ?

The integral of 2x^{3/2} is 4/5 x^{5/2}+C

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integral of 2x^{3/2}

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

\frac{4}{5} x^{\frac{5}{2}} + C

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

= 2 \cdot \frac{2}{5} x^{\frac{5}{2}}

Simplify

2 \cdot \frac{2}{5} x^{\frac{5}{2}} : \frac{4}{5} x^{\frac{5}{2}}

= \frac{4}{5} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{4}{5} x^{\frac{5}{2}} + C

a re a \frac{1}{x}, \frac{1}{x ^{2}}, 1, 2

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

s l o p e in t erce pt (0, 1), (8, 6)

d er i v a t i v e \frac{3 x - 9}{x}

\frac{d y}{d x} = 7 x