Let (I=Integration of 1/x dx). break 1/x as ((1/x)*1),then integrate it. then we get 1=0. Where is wrong?

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- July 7th 2012, 10:02 AMSwarnavintegration
Let (I=Integration of 1/x dx). break 1/x as ((1/x)*1),then integrate it. then we get 1=0. Where is wrong?

- July 7th 2012, 10:19 AMrichard1234Re: integration
...what?

- July 7th 2012, 10:43 PMSwarnavRe: integration
no. try it through by parts method. then I is cancel out from both side.

- July 7th 2012, 11:20 PMProve ItRe: integration
- July 8th 2012, 12:03 AMrichard1234Re: integration
Swarnav's right, letting and , you obtain

I might be wrong, but I'm 99.9% sure that the problem with this method is that you cannot assume that implies . Maybe ? - July 8th 2012, 12:49 AMthesmurfmasterRe: integration
You're right, does not imply but for a constant C. When you integrate by parts you usually don't write this constant out in the intermediate steps because you still have indefinite integrals on both sides. To be strict, however, you should write:

In other words, you can't subtract from both sides, because the constants may be (and in this case are) different. - July 8th 2012, 01:43 AMSwarnavRe: integration
Thanks for helping me.

- July 8th 2012, 05:52 PMrichard1234Re: integration
No problem :)