What's wrong with this integral?

Question

I'm trying to integrate (x)/(d+L-x) respect to x but I get -(d+L)ln(d+L-x) + d + L -x. The correct answer is  -(d+L)ln(d+L-x) -x. What I did was to change the variable u = d + L -x. Then du= -dx. Also, x= d+L-u. Substituting I get ( -(d+L) +u)du/u. I divide the fraction in two, integrate and after substituting (d+L-x) back in u I don't get the correct answer. Any help is much appreciated.

Answer 1

Hi Felipe,

 

You're doing the substitution and the integration perfectly, the only thing is that the extra term of d+L that you're ending up with is a constant, so it'll just get folded into the constant of integration (assuming this is an indefinite integral without limits). The final correct answer should be what you have with a constant of integration (+C) at the end.

 

Best,

Amaan