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

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

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integral from 1 to y of y/x

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

y ln ∣ y ∣

Solution steps

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= y [ln ∣ x ∣]_{1}^{y}

Compute the boundaries:

ln ∣ y ∣

= y ln ∣ y ∣

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\int_{0}^{2 π} cos^{6} (x) d x

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

\int_{3}^{6} (x^{2} - 6 x + 9) d x

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