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March 15th, 2013, 11:39 PM   #1
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4 integration problems

Integrate the following


I tried to solve these many times, but failed. Please help!
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March 16th, 2013, 01:27 AM   #2
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Re: 4 integration problems

2. integral (sin(x)) ^(1/2) dx is not an elementary integral, it can be reduced to an elliptic integral, so you can not express it with elementary functions. See elliptic integrals.
1. you can reduce it sin^(3/2). it's suspicious that the same situation as in 2.
3. substitute y = x^2
4. it's hard to believe you can't solve it.
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March 16th, 2013, 10:50 AM   #3
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Re: 4 integration problems

Number four is nothing more than using differentiation rules. The quotient rule is the one you want to use for that one.
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March 16th, 2013, 04:06 PM   #4
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Re: 4 integration problems

Is the fourth intended to be 1/(5 + 4cos x)? That would be much more interesting.
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March 17th, 2013, 04:52 AM   #5
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Re: 4 integration problems

Quote:
Originally Posted by skipjack
Is the fourth intended to be 1/(5 + 4cos x)? That would be much more interesting.
Yes it's 1/(5+4cos x). I forgot the brackets. I'm terribly sorry.
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March 17th, 2013, 05:06 AM   #6
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Re: 4 integration problems

Thanks a lot csak. Your solutions really worked. I'm grateful to you. Please help me with the 4th one. Actually I forgot the bracket which made it look easy to solve.
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March 18th, 2013, 01:19 AM   #7
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Re: 4 integration problems



Substitute , and :



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March 20th, 2013, 02:57 AM   #8
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Re: 4 integration problems

[reply="Etyucan"]
Thank you so very much!
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