Exercises on Fubini's principle

There are two pieces of integrals (in my collection of past solved problem) that require you to use Fubini's principle to tackle. The previous one is not hard, and similar idea can be applied to the second one, enjoy them.

Integral 1. $\displaystyle \int_0^\infty\frac{\cos x-1}{xe^x}\,d x$.
Numerical answer: -0.34657

Integral 2. $\displaystyle \int_0^1 \frac{\tan^{-1}x}{x\sqrt{1-x^2}}\,d x$.
Numerical answer: 1.3845
(my solution to this one is quite long, and I forgot to extract the solution on the Internet)

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上次金仔堂 totorial 已經俾人抽足成堂。