## hba 3 years ago Integrate

1. hba

$\int\limits _{0}^{\infty} \lfloor x \rfloor e^{-x} dx$

2. hba

I am getting 1/(e-1)

3. Frostbite

absolute value of x right?

4. hba

Right.

5. anonymous

I get 1, but i'll check again

6. Frostbite

Hmm can't do the integral but the aproximation I do get to 1.

7. hartnn

that initially seemed like floor value of x..... :P

8. Frostbite

trid partial integration?

9. hartnn

i also get 1.

10. hba

Yeah one more which i was doing was Integral (x^2/x^2+1) and i got x- arctanx by trig sub.

11. hartnn

thats correct....and can be done without substitution...

12. hartnn

if u can use this integral as standard int 1/(1+x^2) dx = arctan x +c

13. Frostbite

btw forget what I said about partial integration... looks like geting no where.

14. anonymous

after IBP, i get the integral of: $\large [-e^{-x}(x+1)]^\infty_0$ i made the leap that -e^(-x) tends to zero much faster than x+1 tends to infinity as x goes to infinity, but can't give a real justification right now

15. Frostbite

16. anonymous

looks the same, wots 'sign(x)'?

17. Frostbite

The sign function?