1. ## Integration (substitution)

Hey guys first post here .

I have an integration problem, and I thought I had it right, but I guess not lol. Can anyone tell me what I am doing wrong?

integrate: (e^3x)/(e^3x+1)dx or e^3x * 1/e^3x+1*dx

u = e^3x+1
du = e^3x*dx

= 1/u*du

= ln|u|

= ln|e^3x+1|

2. Originally Posted by Ironmaiden22
Hey guys first post here .

I have an integration problem, and I thought I had it right, but I guess not lol. Can anyone tell me what I am doing wrong?

integrate: (e^3x)/(e^3x+1)dx or e^3x * 1/e^3x+1*dx

u = e^3x+1
du = 3e^3x*dx

= 1/u*du

= ln|u|

= ln|e^3x+1|

You're missing something. After you make the substitution, the integral becomes ${\color{red}\tfrac{1}{3}}\int\frac{\,du}{u}$...