What is the integral of (2y)/(y^2) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2y)/(y^2)

\int \frac{2 y}{y ^{2}} d y

2 ln ∣ y ∣ + C

Solution steps

\int \frac{2 y}{y ^{2}} d y

Take the constant out:

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

= 2 \cdot \int \frac{y}{y ^{2}} d y

Cancel the common factor:

y

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

Use the common integral:

\int \frac{1}{y} d y = ln (∣ y ∣)

= 2 ln ∣ y ∣

Add a constant to the solution

= 2 ln ∣ y ∣ + C

\int (4 + x)^{\frac{1}{2}} d x

\int \frac{x + 1}{x ^{2} + 4 x - 5} d x

\int \frac{x - 1}{x ^{3} + 4 x ^{2} + 4 x} d x

\int sin (41 t) sec^{2} (cos (41 t)) d t

\int \frac{1 + x ^{2}}{- 3 x} d x