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# C3: How to integrate? Watch

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1. Afternoon all!
I know how to integrate simple functions like 3x^2 (add one to the power divide by the new power) but I can't do harder ones.
I'm stuck on integrating: (2x+1)/(x) and (2x+1)^2/(x)^2.
Not got a clue where to start
2. (a+b)/c = a/c + b/c
3. (Original post by Get me off the £\?%!^@ computer)
(a+b)/c = a/c + b/c
cheers, i got that bit, its the actual integrating i can't do.
4. (Original post by jim666666)
cheers, i got that bit, its the actual integrating i can't do.
If you mean you are stuck for the integral of 1/x it is ln x. For the second one you could in this case just expand (2x+1)^2 and divide by x^2 and then integrate.
5. Either expand, or treat it as two functions:
f(x) = uv , where u=2x+1, and v=2x^-1

Then f'(x)=u*dv/dx + v*du/dx
6. chain rule? or am i just being stupid saying that? what board are you on?
7. (Original post by luuucyx)
chain rule? or am i just being stupid saying that? what board are you on?
Chain rule is for differentiation we want to integrate the functions given
8. (Original post by anshul95)
Chain rule is for differentiation we want to integrate the functions given
huumm i knew that haha
substitution?
all ive been shown are realllyyy simple ones of these...
9. (Original post by Dark-Myth)
Either expand, or treat it as two functions:
f(x) = uv , where u=2x+1, and v=2x^-1

Then f'(x)=u*dv/dx + v*du/dx
i don't even what
10. (Original post by Pheylan)
i don't even what
I know it's a bit late...
but, it's the chain rule.
11. If it's divide, I'd use the quotient rule?
12. (Original post by Dark-Myth)
I know it's a bit late...
but, it's the chain rule.
actually it's incorrect use of the product rule in a situation where the product rule isn't actually supposed to be used
13. (Original post by Pheylan)
actually it's incorrect use of the product rule in a situation where the product rule isn't actually supposed to be used
OH ****. It's integration. I didn't realise... my baaaad.
We don't do integration in C3, so I thought it was differentiation.
14. (Original post by luuucyx)
huumm i knew that haha
substitution?
all ive been shown are realllyyy simple ones of these...
substution is C4 nice try though
15. (Original post by Get me off the £\?%!^@ computer)
(a+b)/c = a/c + b/c
I am confused? There is no integration in C3
16. (Original post by luuucyx)
chain rule? or am i just being stupid saying that? what board are you on?
LOL
17. (Original post by Faith01)
I am confused? There is no integration in C3
He may be doing a different exam board to what your doing..
18. (Original post by mir3a)
He may be doing a different exam board to what your doing..
Oh yeah that makes sense!
19. (Original post by jim666666)
Afternoon all!
I know how to integrate simple functions like 3x^2 (add one to the power divide by the new power) but I can't do harder ones.
I'm stuck on integrating: (2x+1)/(x) and (2x+1)^2/(x)^2.
Not got a clue where to start
for the first one do.. let f(x)=2x+1/x, then simplify the expression dividing both 2x and 1 by x. so, f(x)=2+x^-1 then integrate as you would normally.

For the second one, let f(x)=(2x+1)^2/x^2, expand the numerator, divide by the denominator as we did above, and integrate
20. (Original post by mir3a)
for the first one do.. let f(x)=2x+1/x, then simplify the expression dividing both 2x and 1 by x. so, f(x)=2+x^-1 then integrate as you would normally.
I think im missing something here, help is appreciated, if you integrate x^-1 its not possible is it? you'd end up dividing by 0 ??

Bear in mind i'm still in AS year and studying C2 atm.

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Updated: December 1, 2010
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