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If f(x)=sqrt(x),g(x)=e^(x)-1, and int...

If `f(x)=sqrt(x)`,`g(x)=e^(x)-1`, and `int fog(x)dx=A fog(x)+B tan^(-1)(fog(x))+C`, then `A+B` is equal to

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` fog(x)=sqrt(e^(x)-1)`
` :. I=int sqrt(e^(x)-1)dx`
`=int(2t^(2))/(t^(2)+1)dt, " where " sqrt(e^(x)-1)=t`
`=2t-2tan^(-1)t+C`
`=2sqrt(e^(x)-1)-2tan^(-1)(sqrt(e^(x)-1))+C`
`=2fog(x)-2tan^(-1)(fog(x))+C`
` :. A+B=2+(-2)=0`
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