Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

integration of log(x^2+2)/(x+2)^2

integration of log(x^2+2)/(x+2)^2

Grade:12th pass

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
7 years ago
Hello Student,
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
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free