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# P3 - ∫ x(3x+1)^-1/2 dx watch

1. plz can u help me qith that question? ∫ x(3x+1)^-1/2 dx (by parts)
2. (Original post by tammypotato)
plz can u help me qith that question? ∫ x(3x+1)^-1/2 dx (by parts)
Nearly finished for tonight but I'll give it a quick go for you....

u = x
du/dx = 1
dv/dx = (3x+1)^-1/2
v = (2/3)(3x+1)^1/2

(2x/3)(3x+1)^1/2 - ∫ (2/3)(3x+1)^1/2
(2x/3)(3x+1)^1/2 (4/27)(3x+1)^3/2
3. (Original post by tammypotato)
plz can u help me qith that question? ∫ x(3x+1)^-1/2 dx (by parts)
I got the following answer... Is it right?
Attached Images

4. (Original post by Leekey)
Nearly finished for tonight but I'll give it a quick go for you....

u = x
du/dx = 1
dv/dx = (3x+1)^-1/2
v = (2/3)(3x+1)^1/2

(2x/3)(3x+1)^1/2 - ∫ (2/3)(3x+1)^1/2
(2x/3)(3x+1)^1/2 (4/27)(3x+1)^3/2
Wow I was right for once You should trust me more tammypotato
5. Mmm, never mind.
6. (Original post by Leekey)
Nearly finished for tonight but I'll give it a quick go for you....

u = x
du/dx = 1
dv/dx = (3x+1)^-1/2
v = (2/3)(3x+1)^1/2

(2x/3)(3x+1)^1/2 - ∫ (2/3)(3x+1)^1/2
(2x/3)(3x+1)^1/2 (4/27)(3x+1)^3/2
thanks

7. (Original post by tammypotato)
thanks

ermm....how? I can't spot my mistake???
8. (Original post by Leekey)
ermm....how? I can't spot my mistake???
its in the p3 book, i dunno!
9. (Original post by tammypotato)
its in the p3 book, i dunno!
Can anyone spot where I went wrong? I thought I was pretty decent at integration-by-parts but apparently that is another thing I can mess up on Wednesday!!!
10. You didn't go wrong. Those two curves are the same...you can rearrange one equation to get the other.
11. (Original post by Leekey)
Can anyone spot where I went wrong? I thought I was pretty decent at integration-by-parts but apparently that is another thing I can mess up on Wednesday!!!
no its all good u just factorised it differently!
12. (Original post by tammypotato)
no its all good u just factorised it differently!
I presume it would be OK left unfactorised tho
13. (Original post by Pixelfairy #1)
I presume it would be OK left unfactorised tho
If they want you to do something with it in the next part of the question then it is usually best not to touch it after integrating by parts.
14. (Original post by Leekey)
If they want you to do something with it in the next part of the question then it is usually best not to touch it after integrating by parts.
Thanks... I never know whether I should be simplifying or not

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Updated: June 6, 2004
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