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Weekly Challenge 24: Suspicious Integrator

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

I asked my integrating application to work out this integral:

Integrate[1000000/(10 + (1000000 - 10)/2^(4*x)), x]

I was given the answer

(25000*Log[-32*(99999 + 16^x)])/Log[2]

Try to evaluate this expression at $x=1$. What has gone wrong? Can you work out the actual real answer and verify by differentiation?
Did you know ... ?

Technology is undoubtedly a very useful mathematical tool, but needs to be used carefully and with some skepticism. If you use a calculating aid it is very important to check that the answer makes sense. Algebraic tools tend not to make errors, but often introduce unnecessary complexity into an answer.