What is the integral of ((2y-5)-y)/(y+xy) ?

The integral of ((2y-5)-y)/(y+xy) is -5/y ln|y+yx|+ln|y+yx|+C

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integral of ((2y-5)-y)/(y+xy)

\int \frac{( 2 y - 5 ) - y}{y + x y} d x

- \frac{5}{y} ln ∣ y + y x ∣ + ln ∣ y + y x ∣ + C

Solution steps

\int \frac{2 y - 5 - y}{y + x y} d x

Take the constant out:

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

= (- 5 - y + 2 y) \cdot \int \frac{1}{y + y x} d x

Simplify

= (- 5 + y) \cdot \int \frac{1}{y + y x} d x

\int \frac{1}{y + y x} d x = \frac{1}{y} ln ∣ y + y x ∣

= (- 5 + y) \frac{1}{y} ln ∣ y + y x ∣

Simplify

(- 5 + y) \frac{1}{y} ln ∣ y + y x ∣ : - \frac{5}{y} ln ∣ y + y x ∣ + ln ∣ y + y x ∣

= - \frac{5}{y} ln ∣ y + y x ∣ + ln ∣ y + y x ∣

Add a constant to the solution

= - \frac{5}{y} ln ∣ y + y x ∣ + ln ∣ y + y x ∣ + C

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

\frac{d}{d x} (2 cos (x) - 2)

\frac{s + 2}{s + 4}

\frac{\partial}{\partial y} (x^{4 y})

x \to - \infty lim (\frac{( 5 x ^{2} - 2 )}{x + 3})

What is the integral of ((2y-5)-y)/(y+xy) ?
The integral of ((2y-5)-y)/(y+xy) is -5/y ln|y+yx|+ln|y+yx|+C