MHB Finding the Primitive of a Complex Integral

[Dustinsfl]

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

 

[Ackbach]

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?

 

[Dustinsfl]

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

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?

 

[Ackbach]

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.