What is the integral of e^{ut} ?

The integral of e^{ut} is 1/u e^{ut}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of e^{ut}

\int e^{u t} d t

\frac{1}{u} e^{u t} + C

Solution steps

\int e^{u t} d t

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

v = u t

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

Add a constant to the solution

= \frac{1}{u} e^{u t} + C