Using WebAssign.com LOST!! I\'m having trouble finding a u-substitute for this o

Question

Using WebAssign.com LOST!! I'm having trouble finding a u-substitute for this one. I just broke it down till I saw something to use as u. It's always the algebra :p

the integrand:

Explanation / Answer

Let 2x = secu => u = sec-1(2x) =>2dx = secutanudu Then sqrt(20x^2-5) = sqrt(5)*(sqrt((2x)^2-1)) = sqrt(5)*tanu =>dx/(x*sqrt(20x^2-5)) = secutanudu/secutanusqrt(5) = du/sqrt(5) =>Integral of dx/(x*sqrt(20x^2-5)) = Integral of du/sqrt(5) = u/sqrt(5) + C But u = sec-1(2x) =>Integral of dx/(x*sqrt(20x^2-5)) = u/sqrt(5) + C = sec-1(2x)/sqrt(5) + C

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