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)

Solved

Posted on 2007-04-09

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 ?

(3/4 ) * (2x* sqrt(1+4^2) +ln (sqrt(1+4^2))

any idea where this result come from ?

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