InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
`int1/(cosx+sqrt(3)sinx)` dx equals |
|
Answer» `int(dx)/(cosx+sqrt3sinx)` `int(sec^2x/2)/(1-tan^2x/2+sqrt3*2tanx/2` `int(sec^2x/2)/(1-tan^2(x/2)+2sqrt3tan(x/2)` Let `tan(x/2)=t` `1/2sec^2(x/2)dx=dt` `int(2dt)/(1-t^2+2sqrt3t)` `int(-2dt)/(t^2-2sqrt3-1)` `-2int(dt)/(t-sqrt3)^2` Let `t-sqrt3=u` `dt=du` `-2int(du)/(u^2-2^2` `-1/2ln((t-sqrt3-2)/(t-sqrt3+2))+c` `-1/2ln|(tan(x/2)-2-sqrt3)/(tan(x/2)+2-sqrt3)|+c`. |
|