Jason Yuhas
Answered
2021-12-31
Answer & Explanation
Mary Goodson
Expert
2022-01-01Added 37 answers
autormtak0w
Expert
2022-01-02Added 31 answers
karton
Expert
2022-01-08Added 439 answers
The answer expands on my comment, which remarked that the integrand of the given integral is twice the Gudermannian function, gd, which appears most famously in the equation governing the Mercator projection in cartography.
NSK
Differentiating the integrand gives
In particular, this derivative is even. Since evaluating the integrand at x=0 gives
for any a: In particular, the occurrence of
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