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

The integral of sqrt(x-2x) is i 1/3 (-x^{3/2}+3xsqrt(x))+C

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integral of sqrt(x-2x)

\int x - 2 x d x

i \frac{1}{3} (- x^{\frac{3}{2}} + 3 x x) + C

Solution steps

\int x - 2 x d x

Simplify

= \int - x d x

Apply Integration By Parts

: x - x - \int - \frac{x}{2 - x} d x

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

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

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

Simplify

x - x - \frac{i x ^{\frac{3}{2}}}{3} : i \frac{1}{3} (- x^{\frac{3}{2}} + 3 x x)

= i \frac{1}{3} (- x^{\frac{3}{2}} + 3 x x)

Add a constant to the solution

= i \frac{1}{3} (- x^{\frac{3}{2}} + 3 x x) + C

y = - 2 x^{3}, (- 1, 2)

\int_{0}^{1} \int_{0}^{1} 4 x y e^{- 2 x - y} d y d x

n = 0 \sum \infty (- 1)^{- n}

\int \frac{8}{17} x^{\frac{17}{9}} + C d x

x \to 3 - lim (\frac{x + 2}{x + 3})

What is the integral of sqrt(x-2x) ?
The integral of sqrt(x-2x) is i 1/3 (-x^{3/2}+3xsqrt(x))+C