$(25$ points$)$ Compute the following integrals

$($a$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{\sqrt[\phantom{2}]{1x^2}}{x}dx$

$($b$){\displaystyle \underset{0}{\overset{1}{}}}\sqrt[\phantom{2}]{x-x^2}dx$

Answer all questions with as much detail as possible, and with all formulas and equations given And why that specific step was used. If possible can you rewrite some other practice questions for me along with the answer with NO solution so i can purely practice it$.$