What is the integral of ye^{xy} ?

The integral of ye^{xy} is e^{yx}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of ye^{xy}

\int y e^{x y} d x

e^{y x} + C

Solution steps

\int y e^{x y} d x

Take the constant out:

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

= y \cdot \int e^{y x} d x

Apply u-substitution

= y \cdot \int \frac{e ^{u}}{y} d u

Take the constant out:

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

= y \frac{1}{y} \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= y \frac{1}{y} e^{u}

Substitute back

u = y x

= y \frac{1}{y} e^{y x}

Simplify

y \frac{1}{y} e^{y x} : e^{y x}

= e^{y x}

Add a constant to the solution

= e^{y x} + C