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August 23rd, 2012, 11:07 AM   #1
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Evaluate the integral

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August 23rd, 2012, 01:30 PM   #2
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What have you tried?
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August 24th, 2012, 10:05 AM   #3
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Re: Evaluate the integral

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August 25th, 2012, 07:10 AM   #4
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Re: Evaluate the integral

Another way to do that is to immediately use to write the integral as
Since that is an odd power of cosine, we can multiply both numerator and denominator by cos(x):

Now let u= sin(x) so that du= cos(x)dx and the integral is

which can be integrated by "partial fractions".
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August 25th, 2012, 11:16 AM   #5
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Re: Evaluate the integral

May I ask something that has nothing to do with the integral at hand?.

zaidalyafey, from where did you get the series in your avatar?.

This appears to be the sum of the reciprocals of the Fibonacci numbers minus the first few terms.

This does not converge to the gamma constant.
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August 26th, 2012, 05:55 AM   #6
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Re: Evaluate the integral

Quote:
Originally Posted by galactus
This does not converge to the gamma constant.


http://www.mymathforum.com/viewtopic.php?f=15&t=32679
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August 26th, 2012, 07:46 AM   #7
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Re: Evaluate the integral

Ok, mathbalarka.

Often times, is used with reference to the sum of the reciprocals of the Fibonacci numbers.

Which is irrational and equal to around 3.359.... or something like that.

I do not like this notation either, as is used for the digamma.
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