b2sonicxh

2022-01-04

How do I integrate the following:

$\int \frac{1+{x}^{2}}{(1-{x}^{2})\sqrt{1+{x}^{4}}}dx$

Stuart Rountree

Beginner2022-01-05Added 29 answers

Let

Then

Now

Thus

Elaine Verrett

Beginner2022-01-06Added 41 answers

Somewhat inspired by Morons

karton

Expert2022-01-11Added 613 answers

Without loss of generality we may assume that 1>x>0. Put

Introduce the new variable

Then we have

Substituting back we obtain

Putting back everything we obtain

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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