What is the integral of (-2sqrt(x)) ?

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

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integral of (-2sqrt(x))

\int (- 2 x) d x

- \frac{4}{3} x^{\frac{3}{2}} + C

Solution steps

\int - 2 x d x

Take the constant out:

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

= - 2 \cdot \int x d x

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

= - \frac{4}{3} x^{\frac{3}{2}} + C

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

\frac{\partial}{\partial x} (2 y x - 3 y + y^{2})

y e^{x y} d x + x e^{x y} d y = 0

\frac{d}{d x} (\frac{a}{b x ^{2}})

2 x

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