Need Help Doing Integation by Parts

And when you post again, @Airp, be sure to include at least some of what you have tried.

 

Also, it's better to include your work right here in the form rather than an image of it. Everything you wrote on paper can be done right here using LaTeX, which isn't really that difficult.

Here is one of the lines from the last image you posted.
$$\frac{z^2e^{z^2}}{2} - \int \frac{2ze^{z^2}dz}{2}$$

The LaTeX script before it is rendered looks like this:
$ $\frac{z^2e^{z^2}}{2} - \int \frac{2ze^{z^2}dz}{2}$ $
Note that I put an extra space between each pair of $ symbols. That prevents the browser from rendering the script.

Fractions: \frac{}{}, with numerator in first pair of braces, and denominator in the second pair
Exponents: Use ^{} after the thing being raised to the power. If the exponent is a single character, the braces aren't needed.
Integrals (indefinite): \int
Integrals (definite): \int_a^b --Here a is the lower limit and b is the upper limit

More info: https://www.physicsforums.com/help/latexhelp/