请教一种求不定积分的方法最近老师说了一种解题方法叫大除法.我有点搞不懂.比如说求t^6/t-1 这个式子的不定积分.我看

如果你不会大除法,也可以用凑的方法：（这里不方便写大除法）
t^6/(t-1)
=(t^6-t^5+t^5-t^4+t^4-t^3+t^3-t^2+t^2-t+t-1+1)/(t-1)
=[t^5(t-1)+t^4(t-1)+t³(t-1)+t²(t-1)+t(t-1)+(t-1)+1)/(t-1)
=t^5 + t^4 + t³ + t² + t + 1 + 1/(t-1)
∫ u²/(u²-2u-3) du
=∫(u²-2u-3+2u+3)/(u²-2u-3)du
=∫1du+∫(2u+3)/(u²-2u-3)du
=u+∫(2u+3)/[(u-3)(u+1)]du
=u-(1/4)∫1/(u+1)du+(9/4)∫1/(u-3)du
=u-(1/4)ln|u+1|+(9/4)ln|u-3|+C
其中：设(2u+3)/(u²-2u-3)=A/(u+1)+B/(u-3)
将右边通分相加后与左边比较系数得：A=-1/4,B=9/4