What is the integral of-x^{5/2} ?

The integral of-x^{5/2} is -2/7 x^{7/2}+C

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integral of-x^{5/2}

\int - x^{\frac{5}{2}} d x

- \frac{2}{7} x^{\frac{7}{2}} + C

Solution steps

\int - x^{\frac{5}{2}} d x

Take the constant out:

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

= - \int x^{\frac{5}{2}} d x

Apply the Power Rule

: \frac{2}{7} x^{\frac{7}{2}}

= - \frac{2}{7} x^{\frac{7}{2}}

Add a constant to the solution

= - \frac{2}{7} x^{\frac{7}{2}} + C

\frac{d y}{d x} - 2 x y^{2} = 0

\int ln ((6 x)^{2}) d x

\int \frac{1}{sin ^{2} ( x )} d x

4 y^{^{''}} + 20 y^{^{'}} + 25 y = 0

y = e^{x}, y = 0, x = 0, x = ln (3)