## 11302 - Hexadecimal Digits of an Integral

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RoBa
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### 11302 - Hexadecimal Digits of an Integral

I think it's very funny, but the formula is rather complicated. Any hints?
Let it be

sclo
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I computed the second sum to be ln(1+x^2), but haven't figured out a closed form for the first product yet. I was never good with working with products.

Tamagodzi
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The hexadecimal expansion of 1/11 isnt 0.0F0F.. that is the hexadecimal expansion of 1/17 ...

goodwill
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The first product is ln2 but i still don't know what is the value of ln(1+x^2)/(x+1)dx

Tamagodzi
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Hint: The result is a wellknown constant

baodog
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Hint:

Bring integral inside the sum,
Integrate before you sum!

sclo
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how do you show that the first product is ln(2)?

Robert Gerbicz
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Probably the fastest way to figure out the constant is to use numeric integration using only say the first 200 terms in the product and in the sum and then from the answer you will know the constant.

You can use PARI-Gp for numeric integration, it's free.
I've used this way in the contest.

goodwill
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AC Finally. Thank you all. Just "guess" the constant.

sclo
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