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

The integral from 1 to 1-2y of y/x is yln|-2y+1|

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integral from 1 to 1-2y of y/x

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

y ln ∣ - 2 y + 1 ∣

Solution steps

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= y [ln ∣ x ∣]_{1}^{1 - 2 y}

Compute the boundaries:

ln ∣ - 2 y + 1 ∣

= y ln ∣ - 2 y + 1 ∣

\frac{d}{d x} (9 x^{2} + y^{2})

y = 5 x^{2}, (4, 80)

x \to - \infty lim (- ln (x))

\frac{d}{d x} (\frac{x}{x ^{2} + 1})

f^{^{'}} (x) = - 2 ln (x) + x^{2} - 4 + e^{x} + x^{e}

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