Homework SourseI am new to these so I need help on a starting place in what
I am new to these so I need help on a starting place in what to look for??I know the inverse functions etc..But, these are different than the earlier integrating where the du would cancel out one of the terms or factors most time..Please direct me..Thank You
Solution
Inverse function integration is an indefinite integration technique. While simple, it is an interesting application of integration by parts. If f and f^(-1) are inverses of each other on some closed interval, then intf(x)dx=xf(x)-intf^(-1)(f(x))f^\'(x)dx, (1) so intf(x)dx=xf(x)-G(f(x)), (2) where G(x)=integrate f^(-1)(x)dx. Therefore, if it is possible to find an inverse f^(-1) of f, integrate f^(-1), make the replacement x->f(x), and subtract the result from xf(x) to obtain the result for the original integral intf(x)dx. If f and f^(-1) are elementary on some closed interval, then intf(x)dx is elementary iff intf^(-1)(x)dx is elementary.
