Find the integral of $x\sin(2x)$ using the table of common integrals rule $\int a\mathrm{d}\xi =a\xi $.
$$x\sin(2x)\xi $$
If $F\left(\xi \right)$ is an antiderivative of $f\left(\xi \right)$, then the set of all antiderivatives of $f\left(\xi \right)$ is given by $F\left(\xi \right)+C$. Therefore, add the constant of integration $C\in \mathrm{R}$ to the result.
