Saved Bookmarks
| 1. |
Evaluate: int(dx)/((x-1)xsqrt(x^(2)-1) |
|
Answer» Solution :`INT(dx)/((x-1)xsqrt(x^(2)-1)) ("put" x-1=1/t rArr dx=-1/t^(2)DT)` `rArr I=int(-1/t^(2)dt)/(1/2sqrt(1/t+1)^(2)-(1/t+1)-1) = int(-dt)/SQRT(-t^(2)+t+1) = int(-dt)/sqrt(sqrt(5)/(2))^(2)-(t-1/2)^(2)` `=-sin^(-1)(t-1/2)/(sqrt(5)/2) + C=-sin^(-1)(2t-1)/(sqrt(5))+C`, where `t=1/(x-1)` |
|