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[tex]\int ln( (x-\frac{1}{2})^2+\frac{7}{4} )dx[/tex]

[tex]u=x-\frac{1}{2}[/tex]

[tex]\int ln(u^2+\frac{7}{4})du[/tex]

[tex]uln(u^2+\frac{7}{4})-\int\frac{2u^2}{u^2+\frac{7}{4}}du[/tex]

[tex]uln(u^2+\frac{7}{4})-ln|u^2+\frac{7}{4}|+C[/tex]

[tex](x-\frac{1}{2})ln(x^2-x+2)-ln|x^2-x+2|+C[/tex]