Integration

Asked by dhawalkushal | 13th Feb, 2019, 08:56: AM

Expert Answer:

integral fraction numerator straight x over denominator square root of straight x squared plus straight x end root end fraction dx
equals 1 half open parentheses integral fraction numerator begin display style 2 straight x plus 1 minus 1 end style over denominator begin display style square root of straight x squared plus straight x end root end style end fraction dx close parentheses
equals fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction open parentheses integral fraction numerator begin display style 2 straight x plus 1 end style over denominator begin display style square root of straight x squared plus straight x end root end style end fraction dx minus integral fraction numerator begin display style 1 end style over denominator begin display style square root of straight x squared plus straight x end root end style end fraction dx close parentheses


integral fraction numerator begin display style 2 straight x plus 1 end style over denominator begin display style square root of straight x squared plus straight x end root end style end fraction dx...................... put space straight x squared plus straight x equals straight t
integral fraction numerator begin display style 1 end style over denominator begin display style square root of straight x squared plus straight x end root end style end fraction dx....... make space perfect space square space in space denominator
integral fraction numerator begin display style 1 end style over denominator begin display style square root of straight x squared plus straight x plus 1 fourth minus 1 fourth end root end style end fraction dx equals integral fraction numerator begin display style 1 end style over denominator begin display style square root of open parentheses straight x plus 1 half close parentheses squared minus open parentheses 1 half close parentheses squared end root end style end fraction dx..... use integral fraction numerator begin display style 1 end style over denominator begin display style square root of straight x squared minus straight a squared end root end style end fraction dx space formula

Answered by Arun | 13th Feb, 2019, 10:01: AM