To plot the functions $f_n(x) = x^n\sin x$ for $n=1,2,3,4$:
import pylab
pylab.rc('text', usetex=True)
x = pylab.linspace(-10,10,1001)
for n in range(1,5):
y = x**n * pylab.sin(x)
y /= max(y)
pylab.plot(x,y, label=r'$x^{}\sin x$'.format(n))
pylab.legend(loc='lower center')
pylab.show()
To make the graphs easier to compare, they have been scaled to a maximum of 1 in the region considered.
