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February 22nd, 2014, 08:58 AM   #1
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Tricky integrals

I need to compute the following integrals. They are really tricky ones? I have solved the first one so far (lol). I tried wolframalpha but you need a pro account to see the full solution. I have looked into different books but i have not found similar ones yet . Can anybody help me?
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February 22nd, 2014, 09:26 AM   #2
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Re: Tricky integrals

Most of them can be done by substitution or "integration by parts". These are the main two integration techniques, so I'm not sure where you've been looking if you haven't found these.
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February 22nd, 2014, 12:58 PM   #3
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Re: Tricky integrals

8. The definite integral from 0 to infinity of -xe^x-e^-x+constant
What do i need to with infinity ?
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February 22nd, 2014, 02:00 PM   #4
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Re: Tricky integrals

You can integrate from 0 to a and take the limit as a -> infinity.
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February 23rd, 2014, 01:04 AM   #5
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Re: Tricky integrals

So is the nr 8 right?
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February 23rd, 2014, 05:23 AM   #6
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Re: Tricky integrals

The correct answer is 1. It seems that you have errors in taking the limit.
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February 23rd, 2014, 07:03 AM   #7
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Re: Tricky integrals

I have solved 1,2 and 8.
I found the solution for the 6th. But i don't understand it
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February 23rd, 2014, 07:27 AM   #8
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Re: Tricky integrals

You can integrate cos(x)^3 using a substitution u = sin(x):





And, you can use the same technique for higher odd powers:





Where you can finish things off using the binomial expansion.
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February 23rd, 2014, 07:58 AM   #9
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Re: Tricky integrals

I had the same solution already on my paper but i thought it could be wrong (lol).

Isn't the 8th one right? Don't look at the last line. The arrow is showing how i opened the brackets.
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February 23rd, 2014, 08:17 AM   #10
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Re: Tricky integrals

The answer to 8 is 1. It's never a good idea to put in as though it is a number. The correct approach is:







are meaningless.
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