Hi
I have this expression but don't know how the answer was reached.
$\displaystyle \int\frac{e^{a/x}}{x^{2}}=-\frac{e^{a/x}}{a}$
I'm sure substitution is involved, this is a weak area for me.
Any help would be greatly appreciated.
Thanks
Hi
I have this expression but don't know how the answer was reached.
$\displaystyle \int\frac{e^{a/x}}{x^{2}}=-\frac{e^{a/x}}{a}$
I'm sure substitution is involved, this is a weak area for me.
Any help would be greatly appreciated.
Thanks
Use the substitution $\displaystyle \frac{a}{x}=t$.
$\displaystyle \frac{1}{x}=\frac{t}{a}\Rightarrow-\frac{1}{x^2}dx=\frac{1}{a}dt\Rightarrow \frac{1}{x^2}dx=-\frac{1}{a}dt$.
Then $\displaystyle \int e^t\left(-\frac{1}{a}\right)dt=-\frac{1}{a}\int e^tdt=-\frac{e^t}{a}+C$
Now replace back t with $\displaystyle \frac{a}{x}$.