so: I know you're supposed to take the limit of the integrals, but I'm having trouble getting started. Without the limits, I found the indefinite integral to be 12arctan(sqrt(x)) +C
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well it converges, but you don't need to split it into two integrals, just put $\displaystyle x=t^2.$
Originally Posted by Krizalid well it converges, but you don't need to split it into two integrals, just put $\displaystyle x=t^2.$ I'm still confused. how would that work?
the substitution? just apply it, can you show what do you get?
just subbing it in would just give $\displaystyle \int\frac{6}{t(1+t^2)}$ would it not?
no it's wrong, try again, the integrand has de arctangent form.
so the integral would be $\displaystyle 12arctan(t)+C$ which is equal to $\displaystyle 12arctan(\sqrt(x))+C$ right? but after finding the integral, what do you do next to find the definite value from 0 to infinity?
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