Solve the Mystery: Find the Logic in These 2 Math Series

Dell
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can anyone see the logic in either of these 2 series?
i have tried everything and cannot get either
the X's are the unknowns

X X 122 21 24 6 10

X 26 14 X 5 3.5 96
 
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I think some terms are missing from the first.
But it looks like it has something to do with division and addition by the same number.
For example:
...
61 * 2 = 122
61 + 2 = 63
63 / 3 = 21
21 + 3 = 24
24 / 4 = 6
6 + 4 = 10
10 / 5 = 2
2 + 5 = 7
...
 
supposing the 63 is really missing, what is the rule here though a n=? i see the number you multiply by/ add goes 2,3,4,5 but the other number goes 61,61,63,21,24,6,10,2 also you have * for the first and / for the rest

how about the second series, X 26 14 X 5 3.5 96 ?
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...

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