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

Simplify

(x)^{3} : (x)^{2} x

= \int (x)^{2} x d x

(x)^{2} = x

= \int x x d x

Simplify

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

= \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

\int 6 x e^{x^{2}} d x

P (t) = - 5 t^{2} + 75 t - 30

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

x \to 1 lim (x^{\frac{7}{1 - x}})