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

The integral of e^{x-y} is e^{-y+x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{x-y}

\int e^{x - y} d x

e^{- y + x} + C

Solution steps

\int e^{x - y} d x

e^{- y + x} = e^{- y} e^{x}

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

Take the constant out:

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

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

Use the common integral:

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

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

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{- y} e^{x} = e^{- y + x}

= e^{- y + x}

Add a constant to the solution

= e^{- y + x} + C

\int t sec^{2} (8 t) d t

\frac{d ^{2} y}{d t ^{2}} + 7 \frac{d y}{d t} + 12 y = 0

\int_{2}^{5} e^{1.5 t} - 2 t d t

\int 1 + \frac{9}{4} x d x

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