JUST INTEGRATION (1 Viewer)

[stressedessert04]

so i get the standard method of changing numerator into 1+e^x - e^x and easily so forth, but at first i thought to times both top and bottom with e^-x and my answer is different and im wondering why?

= integral e^-x/(e^-x +1)
= - integral -e^-x/(e^-x +1)
= -ln|e^x + 1| + C

obviously its missing the x, so im wondering what went wrong in this method and whether its bc x fits in the C = constant section?

 

[ExtremelyBoredUser]

so i get the standard method of changing numerator into 1+e^x - e^x and easily so forth, but at first i thought to times both top and bottom with e^-x and my answer is different and im wondering why?

= integral e^-x/(e^-x +1)
= - integral -e^-x/(e^-x +1)
= -ln|e^x + 1| + C

obviously its missing the x, so im wondering what went wrong in this method and whether its bc x fits in the C = constant section?

They're both the same. I'll modify your result since there's a typo, its supposed to be -ln|e^-x +1| +C

Consider the derivatives of both cases;

multiply by e^x