Integrals dx/( 2x2 – x – 1)

Asked by haroonrashidgkp | 2nd Nov, 2018, 09:45: PM

Expert Answer:

begin mathsize 16px style straight I equals integral fraction numerator dx over denominator 2 straight x squared minus straight x minus 1 end fraction
straight I equals 1 half integral fraction numerator dx over denominator straight x squared minus begin display style straight x over 2 end style minus begin display style 1 half end style end fraction
straight I equals 1 half integral fraction numerator dx over denominator straight x squared minus begin display style straight x over 2 end style plus begin display style 1 over 16 end style minus begin display style 1 over 16 end style minus begin display style 1 half end style end fraction
straight I equals 1 half integral fraction numerator dx over denominator open parentheses straight x minus begin display style 1 fourth end style close parentheses squared minus begin display style 9 over 16 end style end fraction
straight I equals 1 half integral fraction numerator dx over denominator open parentheses straight x minus 1 fourth close parentheses squared minus open parentheses 3 over 4 close parentheses squared end fraction
straight I equals 1 half cross times fraction numerator 1 over denominator 2 cross times begin display style 3 over 4 end style end fraction log space open vertical bar fraction numerator straight x minus 1 fourth minus 3 over 4 over denominator straight x minus 1 fourth plus 3 over 4 end fraction close vertical bar plus straight c
straight I equals 4 over 3 log space open vertical bar fraction numerator 4 straight x minus 4 over denominator 4 straight x plus 2 end fraction close vertical bar plus straight c
straight I equals 4 over 3 log open vertical bar fraction numerator 2 straight x minus 2 over denominator 2 straight x plus 1 end fraction close vertical bar plus straight c end style

Answered by Sneha shidid | 6th Nov, 2018, 10:40: AM