MHB Finding the Primitive of a Complex Integral

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How can I find the primitive of $\int_{\gamma}ze^{z^2}dz$ from $i$ to $2-i$?
 
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dwsmith said:
How can I find the primitive of $\int_{\gamma}ze^{z^2}dz$ from $i$ to $2-i$?

$$\int z e^{z^{2}}\,dz=\frac{1}{2}\int 2z e^{z^{2}}\,dz.$$

Can you finish?
 
Ackbach said:
$$\int z e^{z^{2}}\,dz=\frac{1}{2}\int 2z e^{z^{2}}\,dz.$$

Can you finish?

So $\left(\frac{e^{z^2}}{2}\right)'=\int ze^{z^2}dz$ Then to solve the integral I just integrate g'(z) right?
 
dwsmith said:
So $\left(\frac{e^{z^2}}{2}\right)'=\int ze^{z^2}dz$ Then to solve the integral I just integrate g'(z) right?

Actually, I would have said that

$$\left(\frac{e^{z^{2}}}{2}\right)'=ze^{z^{2}}.$$

Then just use the Fundamenal Theorem of the Calculus, which works because your function is analytic.
 
I posted this question on math-stackexchange but apparently I asked something stupid and I was downvoted. I still don't have an answer to my question so I hope someone in here can help me or at least explain me why I am asking something stupid. I started studying Complex Analysis and came upon the following theorem which is a direct consequence of the Cauchy-Goursat theorem: Let ##f:D\to\mathbb{C}## be an anlytic function over a simply connected region ##D##. If ##a## and ##z## are part of...
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