解：∫(cost)^7dt=∫(cost)^6*costdt=∫(cost)^6dsint=∫(cos²t)³dsint=∫(1-sin²t)³dsint=∫[1-(sint)^6-3sin²t+3sin⁴t]dsint=sint-1/(6+1)(sint)^7-3*1/(1+2)sin³t+3*1/(4+1)(sint)^5+C=sint-(sint)^7/7-sin³t+3(sint)^5/5+C
