Integrating e^x/(e^{2x} + 1): Long Division?

AI Thread Summary
The discussion focuses on the integral ∫(e^x/(e^{2x} + 1) dx and the challenges of rewriting it to fit the arctan formula. Participants suggest that long division may not be necessary, emphasizing the effectiveness of u-substitution, specifically using u = e^x. The conversation highlights the importance of u-substitutions in simplifying integrals and solving problems efficiently. Overall, the consensus is to embrace u-substitution as a valuable tool in integration. Understanding these techniques can significantly ease the process of solving complex integrals.
RadiationX
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i'm having trouble rewriting this integral:\int\frac{e^x}{e^{2x} + 1} so that it will be in the arctan formula: should i use long divison here? if it were not for the e^x in the numerator i'd be fine.
 
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u = e^{x}, du = e^{x}dx

e^{2x} = (e^{x})^2
 
you never get away from u -substitutions do ! thanks
 
Why woudl you watn to get away from them? They save your ass a lot :)
Learn to love em.
 
yeah your right
 
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