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(12)(sqrt(e^(x)-1)dx...

(12)(sqrt(e^(x)-1)dx

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int(e^(x))/(sqrt(e^(2x)-1))dx=

Evaluate: int e^(x)sqrt(e^(2x)+1)dx

int (e^(2x))/(sqrt(e^(x)+1))dx=

int(e^(5x))/(sqrt(e^(5x)+1))dx=

int (dx)/(sqrt(e^(x)-1) ) =

int(dx)/(sqrt(2e^(x)-1))=

int(dx)/(sqrt(e^(x)-1))

int(dx)/(sqrt(e^(2x)-1))=

int(dx)/(sqrt(2e^(x)-1))=

int (dx)/(sqrt(2e^(x)-1))=2 sec^(-1)(sqrt(2)e^((x)/(2)))+c