# [SOLVED]primitive

#### dwsmith

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

#### Ackbach

##### Indicium Physicus
Staff member
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?

#### dwsmith

##### Well-known member
$$\int z e^{z^{2}}\,dz=\frac{1}{2}\int 2z e^{z^{2}}\,dz.$$

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

##### Indicium Physicus
Staff member
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.