Asked by flo
evaluate integral by substitution (e^x-e^(-x))/(e^x+e^(-x))dx
Answers
Answered by
Steve
Note that you have Integral(tanh(x) dx)
= Integral (sinh(x)/cosh(x) dx)
let u = cosh(x)
du = sinh(x) dx
and you have Integral(du/u) = ln(u) = ln(cosh(x)) = ln(e^x + e^-x) + C
Equivalently, let u = e^x + e^-x
Then du = e^x - e^-x du
and you have du/u
= Integral (sinh(x)/cosh(x) dx)
let u = cosh(x)
du = sinh(x) dx
and you have Integral(du/u) = ln(u) = ln(cosh(x)) = ln(e^x + e^-x) + C
Equivalently, let u = e^x + e^-x
Then du = e^x - e^-x du
and you have du/u
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