分类：教育/科学-理工学科-数学
问题：求∫[x^5(2
回答：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.