求e的X次方乘以a的X次方的不定积分
求e的X次方乘以a的X次方的不定积分
数学人气:278 ℃时间:2020-01-31 15:51:17
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答:∫ (e^x)*(a^x) dx=∫ (a^x) d(e^x)=(e^x)*(a^x)-∫ e^x d(a^x)=(ae)^x-∫ (e^x)*(a^x) *(lna) dx所以:(1+lna) ∫ (e^x)*(a^x) dx=(ae)^x所以:∫ (e^x)*(a^x) dx=[(ae)^x]/ln(ea)+C答:∫ (e^x)*(a^x) dx=∫ (a^x) d(e^x) 下一步是分部积分法=(e^x)*(a^x)-∫ e^x d(a^x)=(ae)^x-∫ (e^x)*(a^x) *(lna) dx看第一个和最后一个有:∫ (e^x)*(a^x) dx=(ae)^x-∫ (e^x)*(a^x) *(lna) dx移项:∫ (e^x)*(a^x) dx+ ∫ (e^x)*(a^x) *(lna) dx =(ae)^x合并:(1+lna) ∫ (e^x)*(a^x) dx =(ae)^x所以:∫ (e^x)*(a^x) dx =[(ae)^x]/ln(ae)+C
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