Answer
$-x^{3}cosx+3x^{2}sinx+6xcosx-6sinx+C$
Work Step by Step
Given $\int x^{3}sinxdx$.
You can use the Tabular Method.
Derivative | Anti-derivative
(+)$x^{3}|sinx$
(-)$3x^{2}|-cosx$
(+)$6x|-sinx$
(-)$6|cosx$
(+)$0|sinx$
$=-x^{3}cosx+3x^{2}sinx+6xcosx-6sinx+C$
