What is the integral of-4sqrt(x) ?

The integral of-4sqrt(x) is -8/3 x^{3/2}+C

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integral of-4sqrt(x)

\int - 4 x d x

- \frac{8}{3} x^{\frac{3}{2}} + C

Solution steps

\int - 4 x d x

Take the constant out:

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

= - 4 \cdot \int x d x

Apply the Power Rule

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

= - 4 \cdot \frac{2}{3} x^{\frac{3}{2}}

Simplify

- 4 \cdot \frac{2}{3} x^{\frac{3}{2}} : - \frac{8}{3} x^{\frac{3}{2}}

= - \frac{8}{3} x^{\frac{3}{2}}

Add a constant to the solution

= - \frac{8}{3} x^{\frac{3}{2}} + C

\int - cos (x^{2}) d x

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

(\frac{1}{ln ( x )})^{^{'}}

(2 x + 3)^{^{'}}

\frac{d}{d x} (I n (x^{3} + x))