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

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

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integral from 1 to 2y of (y/x)

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

y ln (2 ∣ y ∣)

Solution steps

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= y [ln ∣ x ∣]_{1}^{2 y}

Compute the boundaries:

ln (2 ∣ y ∣)

= y ln (2 ∣ y ∣)

\int_{4}^{5} x^{2} + x - 9 d x

\int_{2}^{5} 6 d x

\int_{- 1}^{1} 1 + ∣ x ∣ d x

\int_{0}^{2} x x^{2} + 5 d x

\int_{\frac{1}{2}}^{3} \frac{x ^{2} - 1}{x ^{2}} d x

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