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

The integral of e^{(x/2)} is 2e^{x/2}+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/2)}

\int e^{(\frac{x}{2})} d x

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

Solution steps

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

Apply u-substitution

: \int e^{u} \cdot 2 d u

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

Take the constant out:

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

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

Use the common integral:

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

= 2 e^{u}

Substitute back

u = \frac{x}{2}

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

Add a constant to the solution

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

\int \frac{1}{1 - 4 x} d x

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

\int 6 x e^{5 x^{2}} d x

\int 6 x (x - 1) d x

\int 4 x x - 1 d x