Compute:
$\begin{align} \int_{1}^{2}\ x^{9}\ f(2x^{5}-5)\ dx \label{firstintegral}\\\nonumber\end{align}$
and
$\begin{align}\int_{2}^{7}\ f\bigg(\dfrac{5}{x}\bigg)\ dx \label{secondintegral}\\\nonumber\end{align}$
given
$\begin{align*}\int_{\frac{5}{2}}^{\frac{5}{7}}\ \dfrac{f(x)}{x^{2}}\ dx=13 \\\\\int_{\frac{5}{2}}^{\frac{5}{7}}\ \frac{f(x)}{x}\ dx=36 \\\\\int_{-3}^{59}\ f(x)\ dx=9\\\\\int_{2}^{7}\ \dfrac{f(x)}{x^{2}}\ dx=28 \\\\\int_{-3}^{59}\ xf(x)\ dx=46\end{align*}$
There appears to be a lot happening here! Not the least of which is that we do not know $f(x)$, and there appears to be no easy way to find it. But this can be done! Check out the discussion HERE.