Question:

How to solve this ..?

Please answer in steps thank you

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- February 1st 2010, 04:38 AMmj.alawamiIntegrals involving exponential
Question:

How to solve this ..?

Please answer in steps thank you - February 1st 2010, 04:41 AMe^(i*pi)
- February 1st 2010, 04:54 AMtarnishdTry this...
Let =t

x=ln(t)

dx=(1/t)*dt

I=

I= {(1/t)-[1/(t+1)]} dt

I=ln[ex/( ex+1)]+C

I found this proof on the web but verified it in calculation. Seems right to me, hope this helps. - February 1st 2010, 05:33 AMmj.alawami
- February 1st 2010, 05:47 AMe^(i*pi)
I used integration by substituion.

Let - this was chosen to make the denominator easier

When we differentiate u wrt x we get which is obtained through normal rules.

To be able to substitute our du term into the equation we need to isolate dx: . However that isn't very helpful so to get that e^x out the way rearrange the original substitution

(that was a mistake I made in my previous post. It should read the above)

Putting this back into the integral for dx: