What is the integral from 1 to 2x of y/x ?

The integral from 1 to 2x of y/x is yln(2|x|)

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integral from 1 to 2x of y/x

\int_{1}^{2 x} \frac{y}{x} d x

y ln (2 ∣ x ∣)

Solution steps

\int_{1}^{2 x} \frac{y}{x} d x

Take the constant out:

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

= y \cdot \int_{1}^{2 x} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= y [ln ∣ x ∣]_{1}^{2 x}

Compute the boundaries:

ln (2 ∣ x ∣)

= y ln (2 ∣ x ∣)

\frac{d y}{d x}, x y = 2 y + x

f (x) = - x^{3} + x^{2} + 4 x - 2

\frac{d}{d x} (e^{- 3 x} (2 cos (2 x) - 3 sin (2 x)))

x \to 0 lim (\frac{2}{3 - e ^{\frac{1}{x}}})

What is the integral from 1 to 2x of y/x ?
The integral from 1 to 2x of y/x is yln(2|x|)