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(1)/(ae^(x)+be^(-x))...

`(1)/(ae^(x)+be^(-x))`

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`"Let I"=int (1)/(ae^(x)+be^(-x))dx`
`=int (1)/(ae^(x)+((b)/(e^(x))))dx`
`=int(e^(x))/(ae^(2x)+b)dx`
Put `e^(x)=t`
`therefore e^(x)dx=dt`
`therefore I=int(1)/(at^(2)+b)dt`
`=(1)/(a)int (1)/(t^(2)+((b)/(a)))dt`
`=(1)/(a)int(1)/(t^(2)+(sqrt((b)/(1)))^(2))dt`
`=(1)/(a).(1)/(sqrt((b)/(a)))tan^(-1)[(t)/(sqrt((b)/(a)))]+c=(1)/(a).(sqrta)/(sqrtb)tan^(-1)(sqrt((a)/(b)).t)+c`
`=(1)/(sqrtab)tan^(-1)(sqrt((a)/(b)).e^(x))+c`
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