I am posting this here because I don't need help on the whole DE just on this integral..
Here it is:
Please explain.. I can't come up with pi in the denominator..
put $\displaystyle \pi$ inside the integral, and $\displaystyle \frac{1}{\pi}$ outside the integral.
Because they will cancel each other.
i.e. you just multiplied by 1.
See this:
$\displaystyle \int f(x) dx=\int (1) f(x) dx=\int \frac{\pi}{\pi} f(x) dx$
$\displaystyle =\int (\pi) (\frac{1}{\pi}) f(x) dx = \frac{1}{\pi} \int (\pi) f(x) dx$.
By the way, $\displaystyle du=\frac{\pi}{x^2} \;\ {\color{red} dx}$