Integration of bases other than e

[kari82]

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?

 

[snipez90]

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?