Notes: Solve integral:`int (dx)/sqrt(1-e^(2x))`

Sunday, 26 June 2016

Solve integral: $\displaystyle\int\frac{{{\left.{d}{x}\right.}}}{\sqrt{{{1}-{{e}}^{{{2}{x}}}}}}$

$\displaystyle{f{{\left({x}\right)}}}=$
-tanh^-1(sqrt(1-e^(2x)) + C $\displaystyle{i}{s}\neg{a}{n}\in{c}{\quad\text{or}\quad}{r}{e}{c}{t}{s}{o}{l}{u}{t}{i}{o}{n}.$

The derivative of
tanh^-1(x) is $\displaystyle\frac{{1}}{{{1}-{{x}}^{{2}}}}$ .

The solution that you have proposed is just
tanh^-1 expressed on the complex plane.

href="https://en.wikipedia.org/wiki/Inverse_hyperbolic_function">https://en.wikipedia.org/wiki/Inverse_hyperbolic_function

Notes

Sunday, 26 June 2016

Solve integral: $\displaystyle\int\frac{{{\left.{d}{x}\right.}}}{\sqrt{{{1}-{{e}}^{{{2}{x}}}}}}$

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