What is the integral of ((1-2y))/y ?

The integral of ((1-2y))/y is ln|y|-2y+C

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integral of ((1-2y))/y

\int \frac{( 1 - 2 y )}{y} d y

ln ∣ y ∣ - 2 y + C

Solution steps

\int \frac{1 - 2 y}{y} d y

Expand

\frac{1 - 2 y}{y} : \frac{1}{y} - 2

= \int \frac{1}{y} - 2 d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{1}{y} d y - \int 2 d y

\int \frac{1}{y} d y = ln ∣ y ∣

\int 2 d y = 2 y

= ln ∣ y ∣ - 2 y

Add a constant to the solution

= ln ∣ y ∣ - 2 y + C

\int e^{2 x} \cdot sin (2 x) d x

f (x) = x^{2}, at x = - 5

(\frac{1}{s}) (\frac{10}{s + 5})

\frac{3 x + 4}{2 x - 1}

\frac{d}{d x} (4 x^{- \frac{1}{3}})