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

y = e^{x^{2} + 9 x + 4}

y = 3 x^{2}, y = 16 - x^{2}

\int \frac{2}{5 x 9 - 49 x ^{2}} d x

\frac{d x}{d t} = sin (2 t) - 3 x

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