Saved Bookmarks
| 1. |
Integrate: \[ \int \frac{\sin a \cos a}{2 \cos ^{2} a-1} d a \] Show your steps. |
|
Answer» Let I = \(\int {\cfrac{sin a \,cosa}{2cos^2a-1}}{da}\) Put 2cos2 a - 1 = t = - 4 cos a sin a da = dt = sin a cos a da = \(-\cfrac{dt}4\) \(\therefore\) I = \(\cfrac{-1}4\int\) \(\cfrac{dt}t\) = \(\cfrac{-1}4\) lnt + c = \(\cfrac{-1}4\) ln |2cos2 a - 1 | + c (\(\because\) t = 2 cos2 a - 1) |
|