已知f(x)=∫dt/lnt (5为上限,x为下限)求∫(1/x)f(x)dt(5为上限,1为下限)
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![已知f(x)=∫dt/lnt (5为上限,x为下限)求∫(1/x)f(x)dt(5为上限,1为下限)](/uploads/image/z/13345961-41-1.jpg?t=%E5%B7%B2%E7%9F%A5f%28x%29%3D%E2%88%ABdt%2Flnt+%EF%BC%885%E4%B8%BA%E4%B8%8A%E9%99%90%2Cx%E4%B8%BA%E4%B8%8B%E9%99%90%EF%BC%89%E6%B1%82%E2%88%AB%281%2Fx%29f%28x%29dt%EF%BC%885%E4%B8%BA%E4%B8%8A%E9%99%90%2C1%E4%B8%BA%E4%B8%8B%E9%99%90%EF%BC%89)
已知f(x)=∫dt/lnt (5为上限,x为下限)求∫(1/x)f(x)dt(5为上限,1为下限)
已知f(x)=∫dt/lnt (5为上限,x为下限)求∫(1/x)f(x)dt(5为上限,1为下限)
已知f(x)=∫dt/lnt (5为上限,x为下限)求∫(1/x)f(x)dt(5为上限,1为下限)
原式=∫(1,5)dt/lnt∫(1,t)dx/x (做积分顺序变换)
=∫(1,5)[(lnt-ln1)/lnt]dt
=∫(1,5)dt
=5-1
=4.