[tex] \\ \boxed{u = 1-x}
\\
\\ \int _{\:}\:\frac{x^2}{1-x} dx =>
\\
\\ \int \:-\frac{\left(-u+1\right)^2}{u}du
\\
\\ =-\int \frac{\left(-u+1\right)^2}{u}du
\\
\\ =-\int \:u-2+\frac{1}{u}du
\\
\\ =-\left(\int \:udu-\int \:2du+\int \frac{1}{u}du\right)
\\
\\ =-\left(\frac{u^2}{2}-2u+\ln \left|u\right|\right)
\\Scoatem \:\ u =>
\\
\\ =-\left(\frac{\left(1-x\right)^2}{2}-2\left(1-x\right)+\ln \left|1-x\right|\right) [/tex]
[tex] \\ O \:\ putem \:\ simplifica \:\ si \:\ vine:
\\
\\ = -\frac{1}{2}\left(1-x\right)^2+2-2x-\ln \left|1-x\right| =>
\\
\\ = -\frac{\left(1-x\right)^2}{2}+2\left(1-x\right)-\ln \left|1-x\right|
\\
\\ \boxed{ -\frac{\left(1-x\right)^2}{2}+2-2x-\ln \left|1-x\right| + C} [/tex]
