Integrate the following function int_0^1(e^z+1)/(e^z+z dz? Need help with u substitution?

I have already asked this question (socratic link) but I'm not sure how to use u- substitution to get [ln(e^z+z)]_0^1 . Would I start off by letting u=e^z+z? And then du=(e^z+1)dx? Which steps would I need to do next?

1 Answer
Jun 27, 2018

Please see below.

Explanation:

.

int_0^1(e^z+1)/(e^z+z)dz

u=e^z+z

du=(e^z+1)dz

int_0^1(e^z+1)/(e^z+z)dz=int(du)/u=lnabsu=lnabs(e^z+z))_0^1=lnabs(e+1)-lnabs(1+0)=lnabs(e+1)-0=lnabs(e+1)