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Welcome to March Calculus Madness!
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∫ e^x/(e^x + 1) dx
Let z = e^x
Then:
ln z = x
1/z dz = dx
∫ e^x/(e^x + 1) dx
= ∫ z/(z + 1) * 1/z dz
= ∫ 1/(z + 1) dz
= ln |z + 1| + C
= ln |e^x + 1| + C
∫ e^x/(e^x - 1) dx
Again, let z = e^x
∫ e^x/(e^x - 1) dx
= ∫ z/(z - 1) * 1/z dz
= ∫ 1/(z - 1) dz
= ln |z - 1| + C
= ln |e^x - 1| + C
Eddie
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