# Math Help - Integration

1. ## Integration

Pl help me to solve the integral...

$\int \frac{1}{x} e^{-2x} dx$

2. Originally Posted by kjchauhan
Pl help me to solve the integral...

$\int \frac{1}{x} e^{-2x} dx$

This integral has no closed form representation as far as I know...

3. Originally Posted by kjchauhan
Pl help me to solve the integral...

$\int \frac{1}{x} e^{-2x} dx$

I could be wrong, but I don't think this integral has an elementary, closed-form antiderivative.

you may have to use a series representation for $e^{-2x}$.

4. Originally Posted by skeeter
you may have to use a series representation for $e^{-2x}$.
To get started on this, we have

$e^{-2x}=1+(-2x)+\frac{(-2x)^2}{2}+\frac{(-2x)^3}{6}+...$

Divide by $x$ to get $\frac{1}{x}+\sum_{n=1}^{\infty}\frac{(-2)^n x^{n-1}}{n!}$

Integrate this term by term (with respect to $x$).