1.

If int(e^(4x)-1)/(e^(2x))log((e^(2x)+1)/(e^(2x-1)))dx=(t^(2))/(2)logt-(t^(2))/(4)-(u^(2))/(2)logu+(u^(2))/(4)+C, then

Answer»

`u=e^(x)+e^(-x)`
`u=e^(x)-e^(-x)`
`t=e^(x)+e^(-x)`
`t=e^(x)-e^(-x)`

SOLUTION :`I=INT{(e^(2x)-e^(-2x))ln(e^(x)+e^(-x))-(e^(2x)-e^(-2x))ln(e^(x)-e^(-x))}DX`
`=int tln t DT- int u ln u du ("where t"=e^(x)+e^(-x) and u=e^(x)-e^(-x))`
`=(t^(2))/(2)ln t-(t^(2))/(4)-(u^(2))/(2)ln u+(u^(2))/(4)+C`


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