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# Integration by substituition watch

1. Question: Use the substitution x = ln u to find

I'm stuck in the end; here's how I tried to do it:
so

I don't know how to do it after that last step . . .
2. you have the numerator wrong in your last line
3. (Original post by TenOfThem)
you have the numerator wrong in your last line

(Original post by Fing4)
e^(lnu) is not 1
Please see my post carefully, the numerator u is cancelled by 1/u when we replace dx by du/u.
4. (Original post by Zishi)
Please see my post carefully, the numerator u is cancelled by 1/u when we replace dx by du/u.
ooops

5. In that case .... use the standard integral for

6. (Original post by Zishi)
Question: Use the substitution x = ln u to find

I'm stuck in the end; here's how I tried to do it:
so

I don't know how to do it after that last step . . .
Your working is correct so far, ignore the above posts.

Do you know the integrals/derivatives of the inverse trig funtions? You should be able to find one which matches this integral exactly.
7. (Original post by EEngWillow)
Your working is correct so far, ignore the above posts.

Do you know the integrals/derivatives of the inverse trig funtions? You should be able to find one which matches this integral exactly.
Nope, but I guess I can workout derivatives/integrals of their inverse by working out from scratch. To solve this question do I need to learn some of 'em?
8. (Original post by TenOfThem)
In that case .... use the standard integral for

What's the standard integral?
9. (Original post by Zishi)
Nope, but I guess I can workout derivatives/integrals of their inverse by working out from scratch. To solve this question do I need to learn some of 'em?
Pretty much. I think they're in one of the FP modules?

Anyway,

10. As EEngWillow said ... you need to know the differentials of the inverse trig functions

http://www.cliffsnotes.com/study_gui...eId-39884.html

I think you only use tan and sin in C4
11. (Original post by EEngWillow)
Pretty much. I think they're in one of the FP modules?

Anyway,

(Original post by TenOfThem)
As EEngWillow said ... you need to know the differentials of the inverse trig functions

http://www.cliffsnotes.com/study_gui...eId-39884.html

I think you only use tan and sin in C4
Thanks.

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Updated: October 27, 2011
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