What is the integral of e^{(ax)/2} ?

The integral of e^{(ax)/2} is 2/a e^{(ax)/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of e^{(ax)/2}

\int e^{\frac{a x}{2}} d x

\frac{2}{a} e^{\frac{a x}{2}} + C

Solution steps

\int e^{\frac{a x}{2}} d x

Apply u-substitution

= \int \frac{2 e ^{u}}{a} d u

Take the constant out:

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

= \frac{2}{a} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{2}{a} e^{u}

Substitute back

u = \frac{a x}{2}

= \frac{2}{a} e^{\frac{a x}{2}}

Add a constant to the solution

= \frac{2}{a} e^{\frac{a x}{2}} + C

What is the integral of e^{(ax)/2} ?
The integral of e^{(ax)/2} is 2/a e^{(ax)/2}+C