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Hello guys ,I need help on the following which I encountered during reading the book "i:The imaginary tale".

The author writes that Euler evauated that

[tex]

\frac{1}{1^3} + \frac{1}{3^3} + \frac{1}{5^3} + \frac{1}{7^3}+..... = \frac{\pi^2}{4}\ln2 + 2 \int_0^{\pi/2} x ln[sin(x)] dx

[/tex]

He makes the reference that the work can be found in

1) Raymond Ayout-"Euler and the zeta function"-American Mathematical Monthly (dec 1974:pg 1067-86) and

2) Ronald Calinger "Leonhard Euler: The first st. Petersburg years(1727-1741)" Historica Mathematica 23 may 1996 pg 121-166

Since I have access to none of these I am unable to understand how he did it.I shall be grateful to you guys if you could explain or direct me to a webpage for explanation.

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# Evaluation of 1+(1/3^3)+(1/5^3)+

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