Integration of bases other than e

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The discussion focuses on solving the integral ∫(3^(2x))/(1 + 3^(2x)) dx using u-substitution. The substitution u = 1 + 3^(2x) is proposed, leading to the differential du = 2ln(3)[3^(2x)] dx. Participants emphasize the importance of substituting both the numerator and denominator correctly after the change of variables. Clarification is sought on how to handle the numerator in the context of the substitution. The conversation highlights the necessity of careful variable management in integration techniques.
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Find the integral

∫(3^(2x))/(1 + 3^(2x)) dx

so I have that u= 1+3^(2x) and du=2ln3[3^(2x)]

I=1/(2ln3)∫3^(2x)(2)(ln3)/(1 + 3^(2x)) dx

Can anyone help me solve this please?
 
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The point of the u-substitution is so that you make the change of variables and have an easier integrand to work with. Thus you actually need to substitute the u's in. For the denominator of the original integrand, this is clear (look at what substitution you made). Now du = 2 ln(3)[3^(2x)] dx (you need to remember this dx), so do you see how to take care of the numerator now?
 

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