高数求∫1/sint dt

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高数求∫1/sintdt高数求∫1/sintdt高数求∫1/sintdt∫1/sintdt=∫sint/(sint)^2dt=∫-1/(sint)^2dcost=∫-1/(1-(cost)^2)dco

高数求∫1/sint dt
高数求∫1/sint dt

高数求∫1/sint dt
∫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

∫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~