Integral of xcos(pi)xdx d0

1. Rewrite the integrand:

   $$x x \cos{\left(\pi \right)} = - x^{2}$$

2. The integral of a constant times a function is the constant times the integral of the function:

   $$\int \left(- x^{2}\right)\, dx = - \int x^{2}\, dx$$

   1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$:

      $$\int x^{2}\, dx = \frac{x^{3}}{3}$$

   So, the result is: $- \frac{x^{3}}{3}$

3. Add the constant of integration:

   $$- \frac{x^{3}}{3}+ \mathrm{constant}$$

The answer is:

$$- \frac{x^{3}}{3}+ \mathrm{constant}$$