Question

Evaluate x^2-2x-1/(x-1)^2(x^2+1)

Answer 1

Step-by-step explanation:

P=∫x(1−2x)1−x2dx

⇒∫x−2x21−x2dx=∫x(1−2x)1dx−∫x(1−2x)x2dx

⇒∫x(1−2x)1dx−∫1−2xxdx 

Let M=∫x(1−2x)1 & N=∫1−2xxdx

⇒ using partial fraction in M we get

1=A(1−2x)+Bx

1=x(−2A+B)+A

[A=1] & −2A+B=0

[B=2A=2]

Hence

M=∫x1+1−2x2dx=logx+2log(1−2x) & N=∫