How to calculate this?

Question

#int(2x)/((x+2)(x+1))dx#

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Answer 1 · 2018-05-13T06:46:17

#I=4ln|x+2|-2ln|x+1|+c#

Here,

#I=int(2x)/((x+2)(x+1))dx#

Now,
#4(x+1)-2(x+2)=4x+4-2x-4=2x#

#=int((4(x+1)-2(x+2))/((x+2)(x+1))dx#

#=int[(4(x+1))/((x+2)(x+1))-(2(x+2))/((x+2)(x+1))]dx#

#=int[4/(x+2)-2/(x+1)]dx#

#=4int1/(x+2)dx-2int1/(x+1)dx#

#=4ln|x+2|-2ln|x+1|+c#

Answer 2 · 2018-05-13T06:57:14

#= 2 ln ( ((x+2)^2)/(x+1))+ C#

# 2 int \ (x)/((x+2)(x+1))dx#

#= 2 int \ 2/(x+2) - 1/(x+1) \ dx#

#= 2 ( 2ln(x+2) - ln(x+1)) + C#

#= 2 ln ( ((x+2)^2)/(x+1))+ C#