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Problem 71 Hard Difficulty

Evaluate the definite integral.

$ \displaystyle \int^1_0 \frac{e^z + 1}{e^z + z} \, dz $

Answer

$\ln (1+e)$

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Video Transcript

given our into girl we know are you can be even see pussy or the denominator, Which means our d view is eat the C plus Juan D Z because the derivative of Z is just one. Okay, this means our bounds. Now change. We now have eight of zero plus one, which is one on the bottom. And then we have either the one plus one, which is e plus one on the top. You can see our bounds change. Okay, take the enter Growing an integral D over us simply natural log of you using the fundamental theme of calculus. We cannot pull again. You know, the natural love of one simply zero source solution is natural. Log of one pussy.