What is the integral of e^{(-y)/x} ?

The integral of e^{(-y)/x} is -xe^{-y/x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of e^{(-y)/x}

\int e^{\frac{- y}{x}} d y

- x e^{- \frac{y}{x}} + C

Solution steps

\int e^{\frac{- y}{x}} d y

Simplify

= \int e^{- \frac{y}{x}} d y

Apply u-substitution

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

Take the constant out:

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

= - x \cdot \int e^{u} d u

Use the common integral:

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

= - x e^{u}

Substitute back

u = - \frac{y}{x}

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

Add a constant to the solution

= - x e^{- \frac{y}{x}} + C

\int 5 x x d x

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

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

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

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