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

The integral of (((e^x)^2))/((2x)) is 1/2 \Ei(2x)+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))/((2x))

integral

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

\frac{1}{2} Ei (2 x) + C

Solution steps

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

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{( e ^{x} ) ^{2}}{x} d x

(e^{x})^{2} = e^{2 x}

= \frac{1}{2} \cdot \int \frac{e ^{2 x}}{x} d x

Apply u-substitution

: \int \frac{e ^{u}}{u} d u

= \frac{1}{2} \cdot \int \frac{e ^{u}}{u} d u

Use the nonelementary integral:

\int \frac{e ^{x}}{x} d x = Ei (x)

= \frac{1}{2} Ei (u)

Substitute back

u = 2 x

= \frac{1}{2} Ei (2 x)

Add a constant to the solution

= \frac{1}{2} Ei (2 x) + C

y^{3}

(e^{- x})^{3}

sin^{6} (x)

(e^{t})^{2}

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

What is the integral of (((e^x)^2))/((2x)) ?
The integral of (((e^x)^2))/((2x)) is 1/2 \Ei(2x)+C