**1. I am asked to calculate [tex]\int \frac{dx}{cosh(x)}[/tex]**

**2. Relevant equations**

**3. The attempt at a solution**

I know that [tex]\frac{1}{cosh(x)}[/tex] is equivalent to "sech(x)" which by definition is [tex]\frac{2}{e^x+e^{-x}}[/tex].

I'm confused & I don't know which one I need to use for this question:

[tex]\int sech(x) = 2tan{-1}(tanh(\frac{x}{2}))[/tex]

[tex]\int \frac{2}{e^x + e^{-x}} = 2tan^{-1}(e^x)[/tex]

Any help would be greatly appreciated.

I know that [tex]\frac{1}{cosh(x)}[/tex] is equivalent to "sech(x)" which by definition is [tex]\frac{2}{e^x+e^{-x}}[/tex].

I'm confused & I don't know which one I need to use for this question:

[tex]\int sech(x) = 2tan{-1}(tanh(\frac{x}{2}))[/tex]

[tex]\int \frac{2}{e^x + e^{-x}} = 2tan^{-1}(e^x)[/tex]

Any help would be greatly appreciated.

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