## 1018 one year ago integrate 1/x^1.005

1. UnkleRhaukus

first write is as x ^ n

2. UnkleRhaukus

using 1 / x^m = x^-m

3. 1018

yes, x^-1.005. is this right?

4. UnkleRhaukus

good, so you have to integrate it now, (with respect to x, i'm assuming) $\int x^{-1.005}\,\mathrm dx$ are you given limits or not?

5. 1018

yes dx and also i am given the limits, but i am wondering on how to integrate that first.

6. 1018

the limits arent necessary at this moment, am i correct? or is it?

7. UnkleRhaukus

the general case is $\int x^n\,\mathrm dx = \frac{x^{n+1}}{n+1}+c$ for the indefinite integral and $\int\limits_{x_i}^{x_f} x^n\,\mathrm dx = \left.\frac{x^{n+1}}{n+1}\right|_{x=x_i}^{x=x_f}$ for the definite integral

8. UnkleRhaukus

i remember it as: "add one to the index, and divide by the new index"

9. 1018

so the integration is the same before substituting the values of limits right?

10. UnkleRhaukus

yeah, pretty much

11. 1018

yeah, that's what i did, but in the solution i have here, it says its integral is -(200/x^0.005)

12. 1018

im confused by the 200

13. UnkleRhaukus

what did you get?

14. 1018

15. UnkleRhaukus

what is 1/0.005 equal to?

16. 1018

oh wait, is it because 0.005 is 1/200?

17. UnkleRhaukus

yes!

18. 1018

i just entered on the calcu. lol

19. 1018

yeah im having second thoughts lol. maybe the solution made the x the denominator again?

20. 1018

but now im confused where the negative came from. the answer is -(200/x^0.005)

21. UnkleRhaukus

x^(-1.005) x^(-0.005) / -0.005 = -200 x^(-0.005) = -200 / x^(0.005)

22. 1018

oh yes of course i forgot its -0.005 not 0.005. haha. hey thanks man, appreciate the help

23. UnkleRhaukus

if this is the indefinite integral (no limits) don't forget to +c

24. 1018

yup thanks again!