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`int(1+e^(4x))/(4x+e^(4x))^3dx`

`` Let `4x+e^(4x) =t ,`

` 4(1+e^(4x))dx=dt `

`(1+e^(4x))dx=dt/4`

`int(1+e^(4x))/(4x+e^(4x))^3dx`

`=int(dt/4)(1/t^3)=(1/4)intt^(-3)dt`

`=(1/4)(t^(-3+1)/(-3+1))+c`

`=(-1/8)(1/t^2)+c=-1/(4x+e^(4x))^2+c`

Where c is integrating constant.

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