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

The integral of (2x^{3/2})/3 is 4/15 x^{5/2}+C

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integral of (2x^{3/2})/3

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

\frac{4}{15} x^{\frac{5}{2}} + C

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

= \frac{2}{3} \cdot \frac{2}{5} x^{\frac{5}{2}}

Simplify

\frac{2}{3} \cdot \frac{2}{5} x^{\frac{5}{2}} : \frac{4}{15} x^{\frac{5}{2}}

= \frac{4}{15} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{4}{15} x^{\frac{5}{2}} + C

\frac{d y}{d x} = \frac{x ^{2} y ^{2}}{1 + y}

x \to 2 - lim (4 x - 5)

y = 2 e^{x} - e^{x + 1} + e^{\frac{2}{3}} - 5 π^{2}

y^{^{'}} + 10 y = 6

4 t^{2} - 5 sin (3 t)

What is the integral of (2x^{3/2})/3 ?
The integral of (2x^{3/2})/3 is 4/15 x^{5/2}+C