Given $$\int _0^1\left(\int _e^5\frac{dx}{x^2\ln\left(x\right)}\:\right)dy+\int _1^{\ln\left(5\right)}\:\left(\int _{e^y}^5\frac{dx}{x^2\ln\left(x\right)}\:\right)dy$$ Find the sum of the integrals
I'm completely clueless on how I can find the answer here, I do think the integrals don't have a primitive but how can I find the sum here?
The first term is just $$\int _{e}^5\frac{1}{x^2\ln x}dx$$
The second term is
$$\int_1^{\ln 5}\int _{e^y}^5\frac{1}{x^2\ln x}dxdy$$
$$=\int_e^{ 5}\int _{1}^{\ln x}\frac{dx}{x^2\ln x}dydx$$
by change of order.
Can you finish it?