I have never used this method before as my "go to" method. It is pretty cool and seems to have worked like a charm. We have to know that for complex z,n (where n is a complex constant) that:
d[z^n]/dz = n*z^(n-1) - it's been a long time since 2nd year complex analysis.
Or more to the point:
int[x^(i-2)]dx = [x^(i-1)]/[i-1]
and just go after the Im part.
For some reason it never occurred to that for real x, x^i has principle value:
x^i = cos(lnx) + i*sin(lnx)
Now that's cool.
At any rate, you have opened a new door for me. Thanks - Ian.
[-cos(lnx) - sin(lnx)]/[2x]
I have never used this method before as my "go to" method. It is pretty cool and seems to have worked like a charm. We have to know that for complex z,n (where n is a complex constant) that:
d[z^n]/dz = n*z^(n-1) - it's been a long time since 2nd year complex analysis.
Or more to the point:
int[x^(i-2)]dx = [x^(i-1)]/[i-1]
and just go after the Im part.
For some reason it never occurred to that for real x, x^i has principle value:
x^i = cos(lnx) + i*sin(lnx)
Now that's cool.
At any rate, you have opened a new door for me. Thanks - Ian.
can you help me please