Question

高数，不定积分，求这一步的详细解答

Answer 1

面积S=∑<m=0,+∞>{∫<2mπ，(2m+1)π>e^(-x)*sinxdx-∫<(2m+1)π，(2m+2)π>e^(-x)*sinxdx}
=∑<m=0,+∞>{-e^(-x)sinx|<2mπ，(2m+1)π>+∫<2mπ，(2m+1)π>e^(-x)cosxdx
-∫<(2m+1)π，(2m+2)π>e^(-x)*cosxdx}
=∑<m=0,+∞>{-e^(-x)cosx|<2mπ，(2m+1)π>-∫<2mπ，(2m+1)π>e^(-x)sinxdx
+e^(-x)cosx|<(2m+1)π，(2m+2)π>+∫<(2m+1)π，(2m+2)π>e^(-x)*sinxdx}
=∑<m=0,+∞>{e^[-(2m+1)π]+e^(-2mπ)+e^[-(2m+2)π]+e^[-(2m+1)π]
-∫<2mπ，(2m+1)π>e^(-x)sinxdx+∫<(2m+1)π，(2m+2)π>e^(-x)*sinxdx}
所以S=(1/2)∑<m=0,+∞>{e^[-(2m+1)π]+e^(-2mπ)+e^[-(2m+2)π]+e^[-(2m+1)π]}
=(1/2)(1+2/e+1/e^2)/(1-1/e^2)
=(1/2)(e+1)^2/(e^2-1)
=(e+1)/[2(e-1)].

追问

太乱了

Answer 2

题目有哪里?