Can you solve this integral e^2x / (1+e^2x)?
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When you see almost the same thing in the denominator, ln is a good thing to try:
d/dx ln(1 + e^2x) = 2e^2x / (1+ e^2x)
=> d/dx (1/2) ln(1 + e^2x) = e^2x / (1+ e^2x)
d/dx ln(1 + e^2x) = 2e^2x / (1+ e^2x)
=> d/dx (1/2) ln(1 + e^2x) = e^2x / (1+ e^2x)