∫(x^2+5x+4)dx/(x^4+5x^2+a)答案是5/6(ln(x^2+1)(x^2+4)+arctanx+c求详细过程题打错了,a是4

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∫(x^2+5x+4)dx/(x^4+5x^2+a)答案是5/6(ln(x^2+1)(x^2+4)+arctanx+c求详细过程题打错了,a是4

∫(x^2+5x+4)dx/(x^4+5x^2+a)答案是5/6(ln(x^2+1)(x^2+4)+arctanx+c求详细过程题打错了,a是4
∫(x^2+5x+4)dx/(x^4+5x^2+a)
答案是5/6(ln(x^2+1)(x^2+4)+arctanx+c求详细过程
题打错了,a是4

∫(x^2+5x+4)dx/(x^4+5x^2+a)答案是5/6(ln(x^2+1)(x^2+4)+arctanx+c求详细过程题打错了,a是4
确定没有打错题目吗?题目中的a是什么?答案中又怎么没有a?
则:(x^2+5x+4)/(x^4+5x^2+4)=(x^2+5x+4)/(x^2+1)(x^2+4)
=1/(x^2+1)+5x/(x^2+1)(x^2+4)
∫(x^2+5x+4)dx/(x^4+5x^2+a)=∫dx/(x^2+1)+∫5x/(x^2+1)(x^2+4)dx
而∫dx/(x^2+1)=arctanx
∫5x/(x^2+1)(x^2+4)dx=5/2∫d(x^2)/(x^2+1)(x^2+4)
=5/6∫[1/(x^2+1)-1/(x^2+4)]d(x^2)
=5/6[ln(x^2+1)-ln(x^2+4)]
=5/6*ln[(x^2+1)/(x^2+4)]
故∫(x^2+5x+4)dx/(x^4+5x^2+a)
=5/6ln[(x^2+1)/(x^2+4)]+arctanx+c