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1. (Original post by TeeEm)
surely you can simplify it further from that line!!!!

I cannot tell if it is correct until you simplify it fully, but it is looking good
(did you see the limits?)
Yeah I edited it afterwards what limits?
2. (Original post by aersh8)
Yeah I edited it afterwards what limits?
the integral has limits and the answer is in a box at the bottom right
3. (Original post by TeeEm)
the integral has limits and the answer is in a box at the bottom right
strange, this is all I can see:
4. (Original post by aersh8)
strange, this is all I can see:
which integral are you doing?

there are 2

the answer you were showing me was almost the answer of the previous one in post 114
5. (Original post by TeeEm)
which integral are you doing?

there are 2

the answer you were showing me was almost the answer of the previous one in post 114
I'm doing the Lucy one, the Alexandra one had the answer so it was good
6. (Original post by aersh8)
I'm doing the Lucy one, the Alexandra one had the answer so it was good
I took the answer off now! (I left it by mistake)

The Lucy one is tough in the concentration front.
7. (Original post by TeeEm)
I took the answer off now! (I left it by mistake)

The Lucy one is tough in the concentration front.
Ah alright

Is Lucy meant to have limits though?
8. (Original post by aersh8)
Ah alright

Is Lucy meant to have limits though?
no limits on that

the answer you had before was almost the answer to the one in post 114 without limits.

the answer to the one in post 119 is also a neat log
9. (Original post by aersh8)
Spoiler:
Show
(1/4)ln(secx + root(tanx)) + c ?
yes
10. (Original post by TeeEm)
yes
Thanks! Couldn't wait till Saturday to find out :P

How do you even come up with these questions?
11. (Original post by aersh8)
Thanks! Couldn't wait till Saturday to find out :P

How do you even come up with these questions?
those two are dead easy to make.

think of a disgusting function
differentiate it
then give to students to reverse the order, i.e. integrate

Today I am off and I made 2 very hard integrals, for the mathematicians only, i.e no clues
and I am currently working on a third but it is giving me trouble for the last 2 hours
12. (Original post by TeeEm)
those two are dead easy to make.

think of a disgusting function
differentiate it
then give to students to reverse the order, i.e. integrate

Today I am off and I made 2 very hard integrals, for the mathematicians only, i.e no clues
and I am currently working on a third but it is giving me trouble for the last 2 hours
These are really neat when using the substitution though, surely that requires some more thinking?

Are those integrals solve-able using A level maths knowledge? If so please share
13. the first one I have written a solution in two different ways

the second one one method

the third one I am trying to find a sensible method, because the method I have here involves the most ridiculous partial fractions I ever had to do
Attached Images
14. BG.pdf (9.6 KB, 83 views)
15. (Original post by TeeEm)
the first one I have written a solution in two different ways

the second one one method

the third one I am trying to find a sensible method, because the method I have here involves the most ridiculous partial fractions I ever had to do
I did the first one - it took ages so I'm 99.9999% I made a careless mistake along the way

Spoiler:
Show
(39/10)ln(x+1) - (2/5)(rootx) + (3/(x+1)) + c
16. (Original post by aersh8)
I did the first one - it took ages so I'm 99.9999% I made a careless mistake along the way

Spoiler:
Show
(39/10)ln(x+1) - (2/5)(rootx) + (3/(x+1)) + c
sorry but it is not correct.
There is no ln(...) in this one

do you need a hint?
17. (Original post by TeeEm)
sorry but it is not correct.
There is no ln(...) in this one

do you need a hint?
I used u = rootx as a substitution to get:

2*integral(1 + (1/(u^2 + 1)) - (2/((u^2 + 1)^2)) du

and then to integrate that I substituted x back in (so multiplied it all by 1/(2rootx) since du = dx/2rootx), split all that into partial fractions and integrated

does that seem like a correct method? I'm pretty sure I made a mistake in the partial fractions bit since I ran out of paper and had to squeeze it all into the bottom of a page

If there's something wrong with this method then may I please have the hint
18. (Original post by aersh8)
I used u = rootx as a substitution to get:

2*integral(1 + (1/(u^2 + 1)) - (2/((u^2 + 1)^2)) du

and then to integrate that I substituted x back in (so multiplied it all by 1/(2rootx) since du = dx/2rootx), split all that into partial fractions and integrated

does that seem like a correct method? I'm pretty sure I made a mistake in the partial fractions bit since I ran out of paper and had to squeeze it all into the bottom of a page

If there's something wrong with this method then may I please have the hint
The standard way is

u=rootx
then you get partial fractions which are improper, repeated and irreducible!!!!!!
This is very easy to go wrong
Then
you will need to know how to integrate back into an arctan
and then you are done....

Once you achieve the solution in this way then you can see what substitution would clear this mess quicker
19. (Original post by TeeEm)
The standard way is

u=rootx
then you get partial fractions which are improper, repeated and irreducible!!!!!!
This is very easy to go wrong
Then
you will need to know how to integrate back into an arctan
and then you are done....

Once you achieve the solution in this way then you can see what substitution would clear this mess quicker
Thanks!
Did I get the first bit right then (the partial fractions in terms of u)?
What do you mean integrate back into an arctan?
20. (Original post by aersh8)
Thanks!
Did I get the first bit right then (the partial fractions in terms of u)?
What do you mean integrate back into an arctan?

see if you can finish it!!
21. (Original post by TeeEm)

see if you can finish it!!
How would you use arctan though?

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