Интеграл xarctgxdx

[Гост]

∫ xarctgxdx някой може ли да ми помогне с решението моляя важно ми е

[ammornil]

[tex]\int x.arctg(x)dx=\int [\frac{x^2}{2}]'.arctg(x)dx=\int arctg(x)d(\frac{x^2}{2})= \\
=\frac{x^2}{2}.arctg(x)-\int \frac{x^2}{2}d[arctg(x)]=\frac{x^2}{2}.arctg(x)-\frac{1}{2}.\int x^2.\frac{1}{1+x^2}dx=\\
=\frac{x^2}{2}.arctg(x)-\frac{1}{2}.\int \frac{x^2+1-1}{x^2+1}dx= \\
=\frac{x^2}{2}.arctg(x)-\frac{1}{2}.\int\frac{x^2+1}{x^2+1}dx-\frac{1}{2}.\int\frac{-1}{x^2+1}dx=\\
=\frac{x^2}{2}.arctg(x)-\frac{1}{2}.\int1dx+\frac{1}{2}.\int\frac{dx}{1+x^2}=\\
=\frac{x^2}{2}.arctg(x)-\frac{1}{2}.x+\frac{1}{2}.arctg(x)+C=\\
=\frac{1}{2}.arctg(x).(x^2+1)-\frac{1}{2}.x+C[/tex]

[Гост]

∫((7x^3-9)/(x^4-5x^3+6x^2)).dx=?