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Popular Calculus >

integral of (1+y)/y

Solution

\int \frac{1 + y}{y} d y

Solution

ln ∣ y ∣ + y + C

Solution steps

\int \frac{1 + y}{y} d y

Expand

\frac{1 + y}{y} : \frac{1}{y} + 1

= \int \frac{1}{y} + 1 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 1 d y

\int \frac{1}{y} d y = ln ∣ y ∣

\int 1 d y = y

= ln ∣ y ∣ + y

Add a constant to the solution

= ln ∣ y ∣ + y + C

Graph

Popular Examples

integral of xsin(-5x)

\int x sin (- 5 x) d x

integral of 6^{2x}

\int 6^{2 x} d x

integral of 2/(xln(5x))

\int \frac{2}{x ln ( 5 x )} d x

integral of 4/(\sqrt[3]{7x+4)}

\int \frac{4}{3 7 x + 4} d x

integral of 4\sqrt[3]{x^2}

\int 4 3 x^{2} d x

Frequently Asked Questions (FAQ)

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