Нужна помощь[latex] \int\limits^3_1 \frac{dx}{ x^{2} + x^{3} } [/latex]

[latex]\int \frac{1}{x^2+x^3}dx=\int \frac{dx}{x^2(1+x)};\\\\\frac{1}{x^2(1+x)}=\frac{A}{x^2}+\frac{B}{x}+\frac{C}{x+1}=\frac{A(x+1)+Bx(x+1)+Cx^2}{x^2(x+1)}\\\\1=Ax+A+Bx^2+Bx+Cx^2\\\\x^2|B+C=0\\\\x\; |A+B=0\\\\x^0|A=1\\\\B=-A=-1;\; C=-B=1[/latex] [latex]\int _1^3\frac{dx}{x^2+x^3}=\int _1^3\frac{1}{x^2}dx-\int _1^3\frac{1}{x}dx+\int _1^3\frac{dx}{x+1}=\\\\=-\frac{1}{x}|_1^3-ln|x||_1^3+ln|x+1||_1^3=-\frac{1}{3}+1-ln3+ln1+ln4-ln2=\\\\=\frac{2}{3}+ln\frac{4}{6}=\frac{2}{3}+ln\frac{2}{3}[/latex]