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

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

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integral of-x^{3/2}

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

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

Solution steps

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

Take the constant out:

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

= - \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_{- 1}^{1} (x^{3} - x) d x

\int_{0}^{c} 9 e^{3 x} d x

\frac{\partial}{\partial x} (3 sin (2 x y))

x \to \infty lim (e^{8 x})

\frac{d}{d x} ((2 x^{3} + 9 x)^{5})