Please give me the complete solution of 

Asked by Balbir | 23rd Oct, 2017, 08:58: PM

Expert Answer:

begin mathsize 16px style integral fraction numerator 5 straight x over denominator open parentheses straight x plus 1 close parentheses open parentheses straight x squared plus 9 close parentheses end fraction dx
Using space partial space fraction space
fraction numerator begin display style 5 straight x end style over denominator begin display style open parentheses straight x plus 1 close parentheses open parentheses straight x squared plus 9 close parentheses end style end fraction space equals fraction numerator straight A over denominator straight x plus 1 end fraction plus fraction numerator Bx plus straight C over denominator straight x squared plus 9 end fraction
We space get space straight A equals fraction numerator negative 1 over denominator 2 end fraction comma space straight B equals 1 half comma space straight C equals 9 over 2
integral open parentheses fraction numerator negative 1 over denominator 2 open parentheses straight x plus 1 close parentheses end fraction plus fraction numerator begin display style 1 half end style straight x plus begin display style 9 over 2 end style over denominator straight x squared plus 9 end fraction close parentheses dx
integral open parentheses fraction numerator negative 1 over denominator 2 open parentheses straight x plus 1 close parentheses end fraction plus 1 half cross times fraction numerator begin display style straight x plus 9 end style over denominator straight x squared plus 9 end fraction close parentheses dx
integral open parentheses fraction numerator negative 1 over denominator 2 open parentheses straight x plus 1 close parentheses end fraction plus 1 half cross times fraction numerator begin display style straight x end style over denominator straight x squared plus 9 end fraction plus fraction numerator 9 over denominator straight x squared plus 9 end fraction close parentheses dx
Integrate space further space using space formulae.
end style

Answered by Sneha shidid | 15th Dec, 2017, 10:57: AM