Differentiating your result is one technique to validate your own response:d&nbsp;dx&nbsp;(tan−1(sinh(x))=d&nbsp;dx&nbsp;∫∫sec⁡h(x)&nbsp;dx&nbsp;=sec⁡h(x)&nbsp;&nbsp;d&nbsp;dx&nbsp;(tan−1(sinh(x))=11+sinh2(x)×cosh(x)&nbsp;&nbsp;d&nbsp;dx&nbsp;(tan−1(sinh(x)))=1cosh(x)=sec⁡h(x)&nbsp;Because applying the derivative produced the same outcome as the integrand, one can conclude that the method presented is appropriate.

Expert Answer to "Integral of sech(x)"

High School
Geometry
Trigonometry
Trigonometric equations and identities

Kathy Williams

Answered question

2022-01-17

Integral of $s e c h (x)$

Answer & Explanation

aquariump9

Beginner2022-01-18Added 40 answers

Differentiating your result is one technique to validate your own response:
$\frac{d}{d x} (\tan^{- 1} (sinh (x)) = \frac{d}{d x} \int \int \sec h (x) d x = \sec h (x)$
$\frac{d}{d x} (\tan^{- 1} (sinh (x)) = \frac{1}{1 + {sinh}^{2} (x)} \times cosh (x)$
$\frac{d}{d x} (\tan^{- 1} (sinh (x))) = \frac{1}{cosh (x)} = \sec h (x)$
Because applying the derivative produced the same outcome as the integrand, one can conclude that the method presented is appropriate.

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