Google测试员5882
花朵
共回答了13个问题采纳率:69.2% 举报
∫ e^(2x) sinx dx,0 ≤ x ≤ π/2
= (1/2)∫ sinx de^(2x)
= (1/2)e^(2x) sinx - (1/2)∫ e^(2x) d(sinx),分部积分法
= (1/2)e^π - (1/2)∫ e^(2x) cosx dx
= (1/2)e^π - (1/4)∫ cosx de^(2x)
= (1/2)e^π - (1/4)e^(2x) cosx + (1/4)∫ e^(2x) d(cosx),分部积分法
= (1/2)e^π + 1/4 - (1/4)∫ e^(2x) sinx dx
(5/4)∫ e^(2x) sinx dx = (1/2)e^π + 1/4
∫ e^(2x) sinx dx = (2e^π + 1)/5
1年前
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