高数求∫1／sint dt
问题描述：
高数求∫1／sint dt
答
∫1/sint dt
=∫sint/(sint)^2 dt
=-∫d(cost)/[1-(cost)^2]
令u=cost
则有原式=-∫du/(1-u^2)=-1/2∫[1/(1-u)+1/(u+1)]du
=-1/2[ln(1-u)+ln(1+u)]+C
=-1/2ln(1-cost)-1/2ln(1+cost)+C
满意请采纳，谢谢~
答
∫1／sint dt=∫sint ／(sint)^2 dt=∫-1／(sint)^2 dcost=∫-1／(1-(cos t)^2) d cost
=-1∫1／(1-cos t)(1+cos t) d cost=-1/2∫1／(1-cos t)+1/(1+cos t) d cost=-1/2( ln|cost +1|+ln|cost-1|)+C