What is the integral of 2/x y ?

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

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integral of 2/x y

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

2 y ln ∣ x ∣ + C

Solution steps

\int \frac{2}{x} y 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

y = \frac{x ^{2} - 2 x + 5}{x ^{2} + 2 x - 3}

f (x) = 9 - 2 x^{2}, (2, 1)

x \to - 5 lim (\frac{x ^{2} + 3 x - 10}{2 x ^{2} + 15 x + 25})

\int 8 sin^{3} (x) cos^{2} (x) d x