Question

integration of log(1+x)

Answer 1

The question can be solved by using the method of integration by parts. 

Use log(1+x) as one function and 1 as the second function.

hence,

I = ∫(1)*{log(1+x)}  =  {log(1+x)} ∫1dx  -     ∫x/(1+x)dx

Solving this to get

I =  (1+x){log(1+x)}  -  (1+x)