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P3 Integration Challenge watch

1. who can do these?

1. e^xsec^2(e^x) dx
2. 1/xlnx dx
3. 2x/x^4+1 dx

MORE TO COME FOR ALL YOU KEEN BEANS!!!
2. 1) tan(e^x) + C
2) 1/2(lnx)^2 + C
3. 1,3
4. (Original post by Ralfskini)
1) tan(e^x) + C
2) 1/2(lnx)^2 + C
howd you do 2
5. (Original post by kikzen)
howd you do 2
i think ralfskini interpreted the qu. as (1/x).lnx dx
so integrating this would just be a matter of spotting that the differential of (lnx) is (1/x), so you get (1/2)(lnx)^2 +c

I thought the question was like this though: INT 1/(xlnx) dx
For this, I would use the substitution, u=lnx.....and I got ln(lnx) + C as the answer
6. Question 2 is easy peazzzzzy

Intergrate (1/x)lnx

define u= lnx v'= (1/x)
u'=(1/x) v= lnx

{(1/x)lnx.dx = (lnx)^2 - {(1/x)lnx.dx

Simplify by bringin identical integrals together:

2{(1/x)lnx.dx= (lnx)^2

{(1/x)lnx.dx= [(lnx)^2]/2
7. By the way { is my integral symbol
8. (Original post by mathsgeek)
Question 2 is easy peazzzzzy

Intergrate (1/x)lnx

define u= lnx v'= (1/x)
u'=(1/x) v= lnx

{(1/x)lnx.dx = (lnx)^2 - {(1/x)lnx.dx

Simplify by bringin identical integrals together:

2{(1/x)lnx.dx= (lnx)^2

{(1/x)lnx.dx= [(lnx)^2]/2
what the?

i tot the question was

1/(xlnx)
ln x / x
9. 1/xlnx is the same as (1/x)*lnx which is waht i answered dumb arse, lol
10. argh...thats darn weird ya know..
cant seem to understand your working though..
anyways..maybe its the typo which confuses me
11. sorry malasian dude ur right, im the dumb arse
12. (Original post by mathsgeek)
sorry malasian dude ur right, im the dumb arse
no no, it just depends how you read the question,

I mean 1/xlnx dx would appear to mean 1/(xlnx) but according BIDMAS (or whatever you call it) you do division first, so it would be (1/x)*(lnx) - so it just depends on the brackets - so inwhich case you were right
13. (Original post by kikzen)
1,3
Heh, how'd you know about 1/(1 + x^2) being d/dx (arctan x)? If it's Edexcel P3, they wouldn't want that.. wouldn't they want partial fractions or something instead?
14. (Original post by Nylex)
Heh, how'd you know about 1/(1 + x^2) being d/dx (arctan x)? If it's Edexcel P3, they wouldn't want that.. wouldn't they want partial fractions or something instead?
Note to the first poster:- whereabouts should the brackets be for question 2?
15. 1/(xlnx)
16. (Original post by BigJohn)
1/(xlnx)
was my answer right then.....ln(lnx) + C ???
17. It's nice that you guys know the answers, but it would be greta if you could show your working.
I can do most of the Q's in the P3 book but my new tutor (my maths crazy uncle) set me these crazy questions and I can't remember anything since our last lesson.
Next
(x+1)^2e^x
18. I got 1/(2xlnx)
19. (Original post by BigJohn)
It's nice that you guys know the answers, but it would be greta if you could show your working.
I can do most of the Q's in the P3 book but my new tutor (my maths crazy uncle) set me these crazy questions and I can't remember anything since our last lesson.
Next
(x+1)^2e^x
20. Actually I just get 1/2

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