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Help please. Need an explanation on how to do this, have a test tomorrow and don't understand. 

 

∫(e^2x+1)/e^x dx

 

Thanks in advance

Guest Aug 20, 2017
edited by Guest  Aug 20, 2017
 #1
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Do you mean 

 

e^(2x+1)   or   e^(2x)+1     ?

Melody  Aug 20, 2017
 #2
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\(\quad \int(e^{2x}+1)e^{-x}dx\\ =\int (e^x+e^{-x})dx\\ =e^x-e^{-x}+c\)

Melody  Aug 20, 2017
 #3
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\(\quad \int(e^{2x+1})e^{-x}dx\\ =\int(e^{2x+1-x})dx\\ =\int(e^{x+1})dx\\ =\int(e*e^{x})dx\\ =e\int(e^{x})dx\\ =e*e^x+c\\ =e^{x+1}+c\)

Melody  Aug 20, 2017

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