Calculate this integral.

int$(2$x$+1)/(($x$+1)($x$^(2)+$x$+1))$dx

Rubric

Write the partial fraction decomposition with unknown numerators: $1$ mark.

Use common denominator to combine the partial fractions: $2$ marks.

Compare the numerators and solve the system to find the unknown coefficients: $2$ marks. $($You do not

need to show any details of solving the system, and you can solve the system by computer if you wish.$)$

Correctly integrate all the polynomial and linear pieces: $2$ marks.

Split up the quadratic denominator correctly into two pieces with appropriate numerators: $3$ marks.

Integrate the two pieces with quadratic denominators: $2$ marks.

$($Use full sentences to explain each step you take$)$