what is the integral of -4 (1+e^4x)/(4x+e^4x)

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Math

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

`` Let  `t= 4x+e^(4x)`

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

`` Thus integral reduces to

`int(-4(1+e^(4x)))/(4x+e^(4x))dx=int(-1)/t dt=-ln(t)+c`

`=-ln(4x+e^(4x))+c`

`` where c is integration constant.

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