Evaluate: `int1/(2\ e^(2x)+3\ e^x+1)\ dx`

Explanation

I= `int1/(2\ e^(2x)+3\ e^x+1)\ dx`

let,

`e^x=t⇒e^xdx=dt`


`I=int (dt)/(t(1+2t^2+3t))`

`I=int(1/t+1/(1+t)-2/(1+2t))dt`

`I=logt+log(1+t)−2log(1+2t)`

`I=loge^x+log(1+e^x)−2log(1+2e^x)`

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