antiderivative of function of one variable If function is given by y=e^x/(5+e^x), then what is antiderivative?

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To find the anti derivative of y=e^x/(5+e^x) we use substitution.

Let y = 5 + e^x

dy = e^x * dx

Int[ e^x/(5+e^x) dx]

=> Int [(1/y) dy]

=> ln |y| + C

substitute y = 5 + e^x

=> ln |5 + e^x| + C

The required integral of...

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To find the anti derivative of y=e^x/(5+e^x) we use substitution.

Let y = 5 + e^x

dy = e^x * dx

Int[ e^x/(5+e^x) dx]

=> Int [(1/y) dy]

=> ln |y| + C

substitute y = 5 + e^x

=> ln |5 + e^x| + C

The required integral of y=e^x/(5+e^x) is ln |5 + e^x| + C

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