What is the integral of e^{rx} ?

The integral of e^{rx} is 1/r e^{rx}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of e^{rx}

\int e^{r x} d x

\frac{1}{r} e^{r x} + C

Solution steps

\int e^{r x} d x

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = r x

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

Add a constant to the solution

= \frac{1}{r} e^{r x} + C