What is the integral of (zy)/x+zln(y) ?

The integral of (zy)/x+zln(y) is zyln|x|+ln(y)zx+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (zy)/x+zln(y)

\int \frac{zy}{x} + z ln (y) d x

zy ln ∣ x ∣ + ln (y) z x + C

Solution steps

\int \frac{zy}{x} + z ln (y) d x

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{zy}{x} d x + \int ln (y) z d x

\int \frac{zy}{x} d x = zy ln ∣ x ∣

\int ln (y) z d x = ln (y) z x

= zy ln ∣ x ∣ + ln (y) z x

Add a constant to the solution

= zy ln ∣ x ∣ + ln (y) z x + C

What is the integral of (zy)/x+zln(y) ?
The integral of (zy)/x+zln(y) is zyln|x|+ln(y)zx+C