What is the integral of sqrt(x^3) ?

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

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integral of sqrt(x^3)

\int x^{3} d x

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

Solution steps

\int x^{3} d x

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

assuming

x \geq 0

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

Apply the Power Rule

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

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

Add a constant to the solution

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

ln (x^{2} + 1)

\int_{- 2}^{0} \frac{x}{2} + 1 d x

y^{^{'}} = \frac{x e ^{y}}{y}

t^{2} y^{^{''}} - 4 t y^{^{'}} + 6 y = 0

x \to 0 lim (\frac{2 x}{2 x ^{2}})