Hello sage gurus,
Using sage to check a manually calculated integral :
sage: var('r,h')
(r, h)
sage: integrate(r/sqrt(r^2 - sqrt(2)*h*r + h^2), r, 0, sqrt(2)
*h).factor()
sqrt(2)*arcsinh(1)*h
My manual result (using an old table of integrals) was sqrt(2)*ln(sqrt
(2)+1)*h
So, wondering whether arcsinh(1) = ln(sqrt(2)+1), I asked:
sage: bool(arcsinh(1) == ln(1+sqrt(2)))
False
but then,
sage: arcsinh(1).n()
0.881373587019543
sage: ln(1+sqrt(2)).n()
0.881373587019543
They look equal to my eyes...
Also,
sage: bool(arcsinh(1).n() == ln(1+sqrt(2)).n())
False
What am I missing here?
Thanks,
Jim Clark
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