Roger Smith

2022-01-05

Can this integral be solved with contour integral or by some application of residue theorem?

$\int}_{0}^{\mathrm{\infty}}\frac{\mathrm{log}(1+x)}{1+{x}^{2}}dx=\frac{\pi}{4}\mathrm{log}2+\text{}\text{Catalan constant$

eninsala06

Beginner2022-01-06Added 37 answers

For the first integral, we plug

Then it is easy to find that

and hence

For the second integral, we plug

0

Elaine Verrett

Beginner2022-01-07Added 41 answers

If youre

karton

Expert2022-01-11Added 613 answers

In this answer, the substitution

We can use the substitution

which implies

Therefore, we can use

to get

Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function

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