Saved Bookmarks
| 1. |
If C is arbitrary constant then inte^(sin^(-1)x)((lnx)/(sqrt(1-x^(2)))+1/x)dx is equal to |
|
Answer» `e^(SIN^(-1)xcosx)+C` PUT `x=sin theta impliesdx=cos theta d theta` `inte^(theta)((ln sin theta)/(cos theta)+1/(sin theta))cos theta d theta` `=inte^(theta)(ln sin theta+cot theta)d theta=e^(0).ln(sin theta)+c` `=e^(sin^(-1)x) lnx+c=-e^(sin^(-1)In(1/x)+C` |
|