Question

integral(x/x+1)dx

Answer 1

is that \[\int\limits x / (x+1)\]

Answer 2

yeah

Answer 3

integral x/(1+x) dx
For the integrand x/(x+1), do long division:
= integral (1-1/(x+1)) dx
Integrate the sum term by term and factor out constants:
= integral 1 dx- integral 1/(x+1) dx
For the integrand 1/(x+1), substitute u = x+1 and du = dx:
= integral 1 dx- integral 1/u du
The integral of 1/u is log(u):
= integral 1 dx-log(u)
The integral of 1 is x:
= x-log(u)+constant
Substitute back for u = x+1:
= x-log(x+1)+constant