Calculate this integral using integration by parts.

int$($x$^(3)+3$x$^(2)+2$x$+1)$sin xdx

Rubric:

Integration by parts is used multiple times in this question. It is reasonable to explain the process and

strategy once and then implement that strategy multiple times.

Identify the two pieces for integration by parts: $3$ marks.

Correctly implement integration by parts: $6$ marks.

Correctly complete the resulting integrals: $2$ marks.

Clearly explain the previous three calculations: $4$ marks.

Write down every step and show all the work, don$$t skip anything.