∫x/(x^8-1)dx
=∫1/2*(x/(x^4-1)-x/(x^4+1))dx
=1/2∫1/2*(x/(x^2-1)-x/(x^2+1))dx-1/2∫x/(x^4+1)dx
=1/4∫x/(x^2-1)dx-1/4∫x/(x^2+1)dx-1/2∫x/(x^4+1)dx
=1/8∫1/(x^2-1)d(x^2-1)-1/8∫1/(x^2+1)d(x^2+1)-1/4∫1/(x^4+1)d(x^2)
=1/8[ln|x^2-1|-ln(x^2+1)]-1/4arctanx^2+C
=1/8ln|(x^2-1)/(x^2+1)|-1/4arctanx^2+C
这不是高数吧，这是高三数学题吧
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