## anonymous 5 years ago INTEGRAL CALCULUS -Integral of logarithmic functions "Evaluate this integral of (x+3)dx/x+2

1. anonymous

I think you'll have to use long division first since both sides have the same power. The numerator's power must be < the denominator's power. :)

2. anonymous

can u answer it? i want to compare my answer.. please?

3. anonymous

alright, did you do the long division part?

4. anonymous

I got this after diving x+3 / x+2 : 1 + 1/x+2

5. anonymous

dividing*

6. anonymous

is this what you've got?

7. anonymous

my answer x+ln(x+2)+c is this correct?

8. anonymous

hold on , let me finish :)

9. anonymous

yes, excellent :)

10. anonymous

here another example can u answer this

11. anonymous

sure, I'll give it a try ^_^

12. anonymous

integral of xdx/x^2+4

13. anonymous

you can expand the denominator and you'll get the following:$x/(x^2+4) = x/(x+2)^2$ then you'll have to do the partial fractions part which is : $x/(x+2)^2 = A/(x+2) + B/(x+2)^2$....etc correct me if I'm wrong

14. anonymous

you know how to integrate partial fractions, right? :)

15. anonymous

16. anonymous

i dont know

17. anonymous

lol, I have hinted the way for you for you to proceed ^_^

18. anonymous

yes you know :) haven't you taken partial fractions?

19. anonymous

oh wait

20. anonymous

ther's a much simpler way to do it :) hold on no need for partial fractions here

21. anonymous

ur answer? i want to compare my answer

22. anonymous

$\int\limits_{} x/(x^2+4) dx$ let : $u = x^2 +4$ $du = 2x dx$ so : $= 1/2 \int\limits_{} 1/u du$ $= 1/2(\ln |u|) + c$ $=[ \ln|x^2+4|] /2 + c$ sorry abt the complicated mess earlier ^_^

23. anonymous

is this what you've got?

24. anonymous

1/2ln(X^2+4)+C

25. anonymous

yes, well done ^_^

26. anonymous

i wish you can transfer your knowledge in calculus to me

27. anonymous

lol, I was so ignorant in it, but then worked hard to understand it. I took this in the beginning of the semester :), just be patient and practice more then you'll master it ^_^

28. anonymous

do you have facebook i wish we can talk together to practice my enlish

29. anonymous

english

30. anonymous

Unfortunately, I don't have FB, myspace or any of these stuff since I don't have time for them :( , I'm sorry.

31. anonymous

To perfect your english, read more, listen more and communicate more :) that's it

32. anonymous

tnx

33. anonymous

np :)