1. ## improper integral

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

2. well it converges, but you don't need to split it into two integrals, just put $x=t^2.$

3. Originally Posted by Krizalid
well it converges, but you don't need to split it into two integrals, just put $x=t^2.$
I'm still confused. how would that work?

4. the substitution? just apply it, can you show what do you get?

5. just subbing it in would just give $\int\frac{6}{t(1+t^2)}$ would it not?

6. no it's wrong, try again, the integrand has de arctangent form.

7. so the integral would be $12arctan(t)+C$ which is equal to $12arctan(\sqrt(x))+C$ right?

but after finding the integral, what do you do next to find the definite value from 0 to infinity?