请帮我解一道定积分题∫[(x^a)(e^x)]dx.题中a为常数,本题的上限为无穷大,下限为b.你弄错了,应为:f(x,a)=g(a)-a*f(x,a-1)=g(a)-(g(a-1)-(a-1)*f(x,a-2))=……=
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![请帮我解一道定积分题∫[(x^a)(e^x)]dx.题中a为常数,本题的上限为无穷大,下限为b.你弄错了,应为:f(x,a)=g(a)-a*f(x,a-1)=g(a)-(g(a-1)-(a-1)*f(x,a-2))=……=](/uploads/image/z/7788385-1-5.jpg?t=%E8%AF%B7%E5%B8%AE%E6%88%91%E8%A7%A3%E4%B8%80%E9%81%93%E5%AE%9A%E7%A7%AF%E5%88%86%E9%A2%98%E2%88%AB%5B%28x%5Ea%29%28e%5Ex%29%5Ddx.%E9%A2%98%E4%B8%ADa%E4%B8%BA%E5%B8%B8%E6%95%B0%2C%E6%9C%AC%E9%A2%98%E7%9A%84%E4%B8%8A%E9%99%90%E4%B8%BA%E6%97%A0%E7%A9%B7%E5%A4%A7%2C%E4%B8%8B%E9%99%90%E4%B8%BAb.%E4%BD%A0%E5%BC%84%E9%94%99%E4%BA%86%2C%E5%BA%94%E4%B8%BA%3Af%28x%EF%BC%8Ca%29%3Dg%28a%29-a%2Af%28x%EF%BC%8Ca-1%29%3Dg%28a%29-%28g%28a-1%29-%28a-1%29%2Af%28x%EF%BC%8Ca-2%29%29%3D%E2%80%A6%E2%80%A6%3D)
请帮我解一道定积分题∫[(x^a)(e^x)]dx.题中a为常数,本题的上限为无穷大,下限为b.你弄错了,应为:f(x,a)=g(a)-a*f(x,a-1)=g(a)-(g(a-1)-(a-1)*f(x,a-2))=……=
请帮我解一道定积分题
∫[(x^a)(e^x)]dx.题中a为常数,本题的上限为无穷大,下限为b.
你弄错了,应为:
f(x,a)=g(a)-a*f(x,a-1)=g(a)-(g(a-1)-(a-1)*f(x,a-2))=……=
请帮我解一道定积分题∫[(x^a)(e^x)]dx.题中a为常数,本题的上限为无穷大,下限为b.你弄错了,应为:f(x,a)=g(a)-a*f(x,a-1)=g(a)-(g(a-1)-(a-1)*f(x,a-2))=……=
用分部积分
∫[(x^a)(e^x)]dx=∫(x^a)d(e^x)=(x^a)(e^x)-∫(e^x)d(x^a)=(x^a)(e^x)-a∫(x^(a-1))(e^x)dx
设f(x,a)=∫[(x^a)(e^x)]dx,g(a)=(x^a)(e^x)则
f(x,a)=g(a)-f(x,a-1)=g(a)-(g(a-1)-f(x,a-2))=……=g(a)-g(a-1)+g(a-2)+……+((-1)^a)*g(0)
g(0)=(x^0)(e^x)=e^x
不定积分结果是f(x,a)=(x^a-x^(a-1)+……+(-1)^a)(e^x)=x(x^a-(-1)^a)(e^x)/(x+1)
要求定积分就把x的上下限代入f(x,a)中的x.
但这题的被积函数在x趋于无穷时也趋于无穷.所以从b到无穷的反常积分是发散的,积不出来(趋于无穷)
恩,弄错了.不过还是积不出来啊