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Popular >

integral of (1-2y)/y

Solution

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

Solution

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

Popular Examples

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\int_{0}^{2} x p (x - x^{2}) d x

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\frac{s + 1}{( s + 1 ) ^{2} + 5}

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y = x^{5} \cdot x^{4}

derivative of 6sin(x-6xcos(x))

\frac{d}{d x} (6 sin (x) - 6 x cos (x))

y^{^{'}} + x y^{^{''}} = 0

Frequently Asked Questions (FAQ)

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