x^3尀(x^8-2)的不定积分为多少

2025-12-13 22:28:17
推荐回答(1个)
回答1:

1/(x^8-2)=1/[(x^4-√2)*(x^4+√2)]
=√2/4*[1/(x^4-√2)-1/(x^4+√2)]

∫x^3/(x^8-2) dx
=∫1/(x^8-2) d(x^4/4)
=1/4*∫1/(x^8-2) d(x^4)
=1/4*∫√2/4*[1/(x^4-√2)-1/(x^4+√2)] d(x^4)
=√2/16*∫[1/(x^4-√2)-1/(x^4+√2)] d(x^4)
=√2/16*ln|x^4-√2|-√2/16*ln|x^4+√2| +C