## abz_tech 2 years ago integration question

1. abz_tech

$\int\limits\limits_{0}^{1} \frac{ x+1 }{ x ^{2}+6x+5 }dx$

2. Mimi_x3

$x^2+ 6x + 5 = (x+3)^2 -(3)^2 + 5 = (x+3)^2 -9 +5 = (x+3)^2 -1$ $\int\limits \frac{x+1}{(x+3)^{2}-1}$

3. Mimi_x3

Wait. $\frac{x+1}{(x+5)(x+1)} = \frac{A}{(x+5)} +\frac{B}{(x+1)}$ Better now. :D

4. abz_tech

0_o

5. Mimi_x3

For A: $$x= -5$$ $\frac{(-5+1)}{(-5+1)} =\frac{-4}{-4}=1$

6. Hero

Aren't you forgetting something @Mimi_x3 ?

7. Mimi_x3

For B: $$x= -1$$ => $$0$$ What am I forgetting?

8. Hero

$\frac{(x+1)}{(x+5)(x+1)} = \frac{1}{x+5}$

9. Mimi_x3

There is something wrong.

10. abz_tech

isn't u's and du/dx supposed to come into play about now 0_o?

11. Mimi_x3

Oh crap! Sorry!

12. abz_tech

0_o

13. Mimi_x3

So, now $$u= x+5$$

14. Hero

$\int\limits_{0}^{1}(x+5)^{-1}dx$

15. Mimi_x3

I was right anyway :P just went the long way.

16. Hero

Ya, exactly. You're so silly :P

17. Mimi_x3

That doesn't work hero, u = x+5

18. Hero

I can make u = x + 5 if I want or not. It doesn't matter. It will still work.

19. abz_tech

how would u solve (x+5)^-1

20. abz_tech

$\ln x+5?$

21. winterfez

no i guess that does not work

22. Mimi_x3

$\int\limits\frac{1}{x+5}dx$ $u = x+5 => \frac{du}{dx} = 1 => du = dx$ $\int\limits\frac{1}{u} du = \ln(x+5) + C$ @hero: writing in that form won't work.

23. Hero

$\ln(|x+5|)$

24. Hero

I don't need @mimi_x3 ( a kid) to tell me things, lol

25. winterfez

@hero right, is absolute value for ln

26. Mimi_x3

I am not a kid!! It's the truth it won't work in the form; of if you want to use that retarded formula.

27. abz_tech

hero how would u go about doing $\int\limits_{0}^{1} (x+5)^{-1}$

28. Mimi_x3

Using that form; wont get you anyway; and get lost.

29. abz_tech

fine mimi, can u tell me your way =/?

30. Hero

She already did. @winterfez, also provided some good steps.

31. Mimi_x3

i typed up the solution!!! scroll upp!!

32. Hero

I think I deserve a medal for pointing @mimi_x3 in the right direction.

33. abz_tech

then with the limits would i be ln 6 - ln 5?

34. Mimi_x3

Well, first I was not wrong,I just went the long way. I would have gotten the right anwer without your input. Secondly, can you please show us how you would integrate $\int\limits(x+5)^{-1} dx$

35. Hero

That's top secret info.

36. Mimi_x3

Lol, because it's impossible :)

37. Mimi_x3

Me want a medal as well!

38. Hero

Nothing is impossible

39. Mimi_x3

:D