What is the integral of 1/(sqrt(cosh(x)-sinh(x))) ?

The integral of 1/(sqrt(cosh(x)-sinh(x))) is 2/(sqrt(cosh(x)-sinh(x)))+C

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integral of 1/(sqrt(cosh(x)-sinh(x)))

\int \frac{1}{cosh ( x ) - sinh ( x )} d x

\frac{2}{cosh ( x ) - sinh ( x )} + C

Solution steps

\int \frac{1}{cosh ( x ) - sinh ( x )} d x

Apply u-substitution

= \int - \frac{2}{u ^{2}} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 2 \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

= - 2 (- \frac{1}{u})

Substitute back

u = cosh (x) - sinh (x)

= - 2 (- \frac{1}{cosh ( x ) - sinh ( x )})

Simplify

- 2 (- \frac{1}{cosh ( x ) - sinh ( x )}) : \frac{2}{cosh ( x ) - sinh ( x )}

= \frac{2}{cosh ( x ) - sinh ( x )}

Add a constant to the solution

= \frac{2}{cosh ( x ) - sinh ( x )} + C

What is the integral of 1/(sqrt(cosh(x)-sinh(x))) ?
The integral of 1/(sqrt(cosh(x)-sinh(x))) is 2/(sqrt(cosh(x)-sinh(x)))+C