∫(x^3)*(x^2+1)^1/2的积分是什么.我有点知道要用三角代换...但是还不是很清楚.

令x=tant ,cost=(1+x^2)^(-1/2)
∫(x^3)*(x^2+1)^1/2dx=∫(tant)^3*sectdtant
=∫(tantsect)^3dt
=∫(sint)^3/(cost)^6dt
=-∫(sint)^2/(cost)^6dcost
=∫((cost)^2-1)/(cost)^6dcost
=∫1/(cost)^4dcost-∫1/(cost)^6dcost
=(-1/3)(cost)^(-3)+(1/5)(cost)^(-5)+C
=(-1/3)(1+x^2)^(3/2)+(1/5)(1+x^2)^(5/2)+C

∫(x^3)*(x^2+1)^1/2dx
=1/2∫(x^2)*(x^2+1)^1/2dx^2(令y=x^2)
=1/2∫y*(y+1)^1/2dy
=1/2∫（y+1-1）*(y+1)^1/2dy
=1/2{∫（y+1）*(y+1)^1/2dy-∫(y+1)^1/2dy}
=1/2{∫（y+1）*(y+1)^1/2d（y+1）-∫(y+1)^1/2d（y+...