What is the indefinite integral of f(x)=e^x/(e^2x +1)?

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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We'll solve the integral using substitution technique.

Let e^x = t => e^x dx = dt

`int` e^x dx/(e^2x +1) = `int` dt/(t^2 + 1) = arctan t + C

`int` e^x dx/(e^2x +1) = arctan e^x + C

The requested result of the indefinite integral is represented by the primitive function F(x) = arctan e^x + C, where C represents the family of constants.

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