en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Popular Examples

integral of 4/((4x-2)ln(4x-2))

\int \frac{4}{( 4 x - 2 ) ln ( 4 x - 2 )} d x

integral of xsin(-5x)

\int x sin (- 5 x) d x

integral of 6^{2x}

\int 6^{2 x} d x

integral of cos^4(x)sin(2x)

\int cos^{4} (x) sin (2 x) d x

integral of 4/(100+x^2)

\int \frac{4}{100 + 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