## Asylum15 3 years ago - Integral!

1. Asylum15

$\int\limits \frac{ lnx }{ x }$

2. Asylum15

Whos feelin brave? :D

3. TuringTest

I'm thinking by parts...

4. surdawi

u du

5. Siddharth18

do it by substitution, let lnx= u

6. TuringTest

haha, oh yeah, I overthought it :P

7. Asylum15

Can U be lnx ? It's above the line

8. TuringTest

so?

9. surdawi

|dw:1353166961045:dw|

10. Siddharth18

|dw:1353035523772:dw|

11. waterineyes

Put ln(x) = u So: $$\frac{1}{x} \cdot dx =du$$

12. Asylum15

Thank you guys

13. waterineyes

Just try and if you face any problem, then do ask us...

14. Asylum15

Wait, can you expand on that for me? I have $dx = \frac{ du }{ 1/x }$

15. waterineyes

Are you converting a simple solution to hard one??

16. Asylum15

Looks like it xD

17. waterineyes

|dw:1353167337486:dw|

18. waterineyes

Sorry, my handwriting is not too good..

19. Asylum15

Is this a direct manipulation or a substitution?

20. waterineyes

Is this not Substitution ?? We are substituting u in place of x..

21. Asylum15

Ah, ok, so lnx. Differentiation of ln = 1 over So 1/x right?

22. waterineyes

Yes..

23. waterineyes

$\frac{d}{dx}\ln(x) = \frac{1}{x}$

24. Asylum15

So, let me just clarify. lnx / x = 1/x?

25. Asylum15

Where does the x under the line go?

26. waterineyes

See : $\ln(x) = u$ Right ??

27. Asylum15

Yes

28. waterineyes

Now take derivative both the sides and tell what did you get??

29. Asylum15

Next, i've been taught to do du/dx

30. Asylum15

1/x . dx

31. waterineyes

Write them properly.. with LHS and RHS..

32. Asylum15

Little lost here, sorry :(

33. Asylum15

1/x . dx = du

34. waterineyes

Do you know how it came??

35. Asylum15

Yes i get this.

36. Asylum15

What is the next step?

37. waterineyes

Just use this to substitute these values in your question..

38. Asylum15

I think the way i've been taught is conflicting... I usually write dx = du / 1/x

39. Asylum15

If substituting