What is the integral of x((4e^{x^2})/(x^2)) ?

The integral of x((4e^{x^2})/(x^2)) is 2\Ei(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 x((4e^{x^2})/(x^2))

\int x (\frac{4 e ^{x^{2}}}{x ^{2}}) d x

2 Ei (x^{2}) + C

Solution steps

\int x \frac{4 e ^{x^{2}}}{x ^{2}} d x

Take the constant out:

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

= 4 \cdot \int x \frac{e ^{x^{2}}}{x ^{2}} d x

Simplify

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

= 4 \cdot \int \frac{e ^{x^{2}}}{x} d x

Apply u-substitution

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

= 4 \cdot \int \frac{e ^{u}}{2 u} d u

Take the constant out:

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

= 4 \cdot \frac{1}{2} \cdot \int \frac{e ^{u}}{u} d u

Use the nonelementary integral:

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

= 4 \cdot \frac{1}{2} Ei (u)

Substitute back

u = x^{2}

= 4 \cdot \frac{1}{2} Ei (x^{2})

Simplify

4 \cdot \frac{1}{2} Ei (x^{2}) : 2 Ei (x^{2})

= 2 Ei (x^{2})

Add a constant to the solution

= 2 Ei (x^{2}) + C

\int ln (x) x^{8} d x

\int \frac{t t + 6 t}{t ^{2}} d t

\int 2 t^{3} e^{t^{2}} d t

\int 5 x (\frac{4}{x} + \frac{3}{x ^{2}}) d x

\int \frac{3}{x ^{4} - 16} d x

What is the integral of x((4e^{x^2})/(x^2)) ?
The integral of x((4e^{x^2})/(x^2)) is 2\Ei(x^2)+C