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# evaluate integral of ( sqrt (1+4x^2 ))

Posted on 2007-04-09
Medium Priority
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i am working on a problem and i am stuck on the integral of ( sqrt (1+4x^2 ))  which somehow turns out to

(3/4 ) * (2x* sqrt(1+4^2) +ln (sqrt(1+4^2))
any idea where this result come from ?
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Question by:c_hockland
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Accepted Solution

aburr earned 2000 total points
ID: 18876467
Some suggestions.
Factor the 4 out so you get 2*sqr(x^2 + ¼)
Now try substitution
z = ¼ + x^2  and interagte by parts
Or
z = arsinh ( 4x) so that sqr (x^2 + ¼) = (1/4)*cosh(z)
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Author Comment

ID: 18877236
oh, yes, didnt thhink of by parts integration.
ok, thanks aburr...
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