What is the integral of (-2y)/x ?

The integral of (-2y)/x is -2yln|x|+C

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integral of (-2y)/x

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

- 2 y ln ∣ x ∣ + C

Solution steps

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

Take the constant out:

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

= - 2 y \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= - 2 y ln ∣ x ∣

Add a constant to the solution

= - 2 y ln ∣ x ∣ + C

x \to 5 + lim (\frac{- 3}{x ^{2} - 25})

(1 + x^{2}) y^{^{'}} = x (1 - y)

1 + 4 x - x^{2}, 11 - x - x^{2}, 1 - \frac{2 x}{3}

x + 1, 2 x - 4, 0, 3

\int \frac{3 x ^{5} - 2}{4 x - 4 x ^{5}} d x