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How do I Integrate this! u substitution with limits. 
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#1
Feb2112, 04:15 AM

P: 134

1. The problem statement, all variables and given/known data
Find ∫e^x/ (1+e^2x). dx , with limits ln 2 & 0 given u= e^x 2. Relevant equations 3. The attempt at a solution u= e^x du/dx = e^x dx= du/e^x sub limits of ln2 & 0 → u Hence, limits 2 & 1 Therefore, ∫u* (1+e^2x)^1* du/e^x = ∫ u/ (u + e^3x) = ∫ u/ e^3x = ∫ 1/e^2x = e^x = 1/u plugging in limits of 2 &1 Therefore, 0.2325... Although i could not find this on the answer sheet did i do something wrong? Please help, Thankyou. 


#2
Feb2112, 06:06 AM

P: 38

Should it become this?
[itex]\int^{2}_{1}(1+u^{2})^{1}du[/itex] = [itex]\left[\frac{ln(1+u^{2})}{2u}\right]^{2}_{1}[/itex] 


#3
Feb2112, 06:16 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,301

Instead, look up the derivative of arctan(u). 


#4
Feb2112, 09:06 AM

P: 38

How do I Integrate this! u substitution with limits.
Oops haha
should let u = tanθ 


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