∫ dx / (2e^2x + 3e^x +1)

Asked by sunil2791 | 3rd Oct, 2017, 07:25: PM

Expert Answer:

begin mathsize 16px style integral fraction numerator dx over denominator 2 straight e to the power of 2 straight x end exponent space plus space 3 straight e to the power of straight x space plus space 1 end fraction
Consider comma
2 straight e to the power of 2 straight x end exponent space plus space 3 straight e to the power of straight x space plus space 1
straight e to the power of straight x space equals space straight t
2 straight t squared space plus 3 straight t space plus space 1
2 straight t squared space plus space 2 straight t space plus space straight t space plus space 1
2 straight t open parentheses straight t space plus space 1 close parentheses plus space open parentheses straight t space plus space 1 close parentheses
open parentheses straight t space plus space 1 close parentheses open parentheses 2 straight t space plus space 1 close parentheses
rightwards double arrow open parentheses straight e to the power of straight x space plus space 1 close parentheses open parentheses 2 straight e to the power of straight x space plus space 1 close parentheses
integral fraction numerator begin display style dx end style over denominator begin display style open parentheses straight e to the power of straight x space plus space 1 close parentheses open parentheses 2 straight e to the power of straight x space plus space 1 close parentheses end style end fraction
Solve space this space using space partial space fraction space method.
end style

Answered by Sneha shidid | 28th Dec, 2017, 10:14: AM