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Grade: 12th pass
        log(x^2+2)/(x+2)^2
6 years ago

Answers : (1)

Rinkoo Gupta
askIITians Faculty
80 Points
							Integral log(x^2+2)/(x+2)^2dx
integrating by part by taking log(x^2+2) as first function and 1/(x+2)^2 as second function
=>-(log(x^2+2).)/(x+2)+integral{2x/(x^2+2).(x+2)}dx
using partial fraction
let x/(x^2+2)(x+2)=A/(x^2+2)+B/(x+2)
=>x=A(x+2)+B(x^2+2)
put x=-2 we get
-2=B(4+2)=6B
=>B=-2/6=-1/3
put x=0
0=2A+2B
=>0=2A-2/3=>2A=2/3=>A=1/3
Hence the solution is
-(log(x^2+2))/(x+2)+2integral{1/(3(x^2+3))-1/(3(x+2))}dx
=-(log(x^2+2))/(x+2)+2/3{arctan(x/root2)-logmod(x+2)}

Thanks & Regards
Rinkoo Gupta
AskIITians Faculty

6 years ago
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