\(\int \left(1-2x^{2} \right)^{3} x^{2} {\rm d}x =\int \left(1-6x^{2} +12x^{4} -8x^{6} \right)x^{2} {\rm d}x\, \)
\({\rm =}\int \left(x^{2} -6x^{4} +12x^{6} -8x^{8} \right){\rm d}x \)
\(=\frac{x^{3} }{3} -\frac{6x^{5} }{5} +\frac{12x^{7} }{7} -\frac{8x^{9} }{9} +C\)