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int(e^(6logx)-e^(5logx))/(e^(4logx)-e^(3...

`int(e^(6logx)-e^(5logx))/(e^(4logx)-e^(3logx))dx`

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Let ` I = int((e^(6logx)-e^(5logx))/(e^(4logx)-e^(3logx)))dx`
`=int((e^(logx^(6))-e^(logx^(5)))/(e^(logx^(4))-e^(logx^(3))))dx , [:'alogb = logb^(a)]`
`=int((x^(6)-x^(5))/(x^(4)-x^(3)))dx , [:'e^(logx)=x]`
`= int((x^(3)-x^(2))/(x-1))dx=int(x^(2)(x-1))/(x-1)dx`
`= intx^(2)dx = (x^(3))/(3)+C`
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