求∫[x^5(2
令2-5x^3=t,则x^3=(2-t)/5, ∴x^5dx=1/3*x^3d(x^3)=-1/75*(2-t)dt ∴∫[x^5(2-5x^3)^(2/3)]dx =-1/75*∫[t^(2/3)*(2-t)]dt =-1/75*∫[2t^(2/3)-t^(5/3)]dt =-2/125*t^(5/3)+1/200*t^(8/3)+C =-(6+25x^3)/1000*(2-5x^3)^(5/3)+C.