What is the integral from 1 to 2 of x/y+y/x ?

The integral from 1 to 2 of x/y+y/x is xln(2)+3/(2x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 1 to 2 of x/y+y/x

\int_{1}^{2} \frac{x}{y} + \frac{y}{x} d y

x ln (2) + \frac{3}{2 x}

Solution steps

\int_{1}^{2} \frac{x}{y} + \frac{y}{x} 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_{1}^{2} \frac{x}{y} d y + \int_{1}^{2} \frac{y}{x} d y

\int_{1}^{2} \frac{x}{y} d y = x ln (2)

\int_{1}^{2} \frac{y}{x} d y = \frac{3}{2 x}

= x ln (2) + \frac{3}{2 x}

What is the integral from 1 to 2 of x/y+y/x ?
The integral from 1 to 2 of x/y+y/x is xln(2)+3/(2x)