# Thread: complex analysis - integration

1. ## complex analysis - integration

If having to integrate a conjugate do you multiply the function by the differential of the normal function or the differential of the conjugate?
e.g.integrate the real conjugate of t^3 -it. Thanking you in advance for any help.

2. Originally Posted by Ruth
If having to integrate a conjugate do you multiply the function by the differential of the normal function or the differential of the conjugate?
e.g.integrate the real conjugate of t^3 -it. Thanking you in advance for any help.
Do you mean "integrate a conjugate" or "take the conjugate of the integral"?

If you mean "integrate a conjugate" then it is simply $\int \overline{f}(z)dz$.

If you mean take "the conjugate of the integral" then $\overline{\int f(z)dz}= \int \overline{f}(z)d\overline{z}$.

3. ## integrating conjugates

Thank you - it was the first I meant and I wasn't sure what to do - thought you had to integrate the function and then multiply by the derivative of the function according to cauchy's Integral theorem but didn'tknow if the derivtive was before or after finding the conjugate. How does everyone manage to type the mathematical stuff ?