u = 1+x³,du = 3x² dx∫ (1+x³)^(3/2) * x^5 dx= (1/3)∫ u^(3/2) * (u-1) du= (1/3)∫ [u^(5/2) - u^(3/2)] du= (1/3) * [u^(5/2+1) / (5/2+1) - u^(3/2+1) / (3/2+1)] + C= 2/21*(1+x³)^(7/2)...