Verify the integration formula.
-$$\int 2 \operatorname { sech } x d x = \sin ^ { - 1 } \left( 1 - x ^ { 2 } \right) + C$$

Name: Verify the integration formula. -\[\int 2 \operatorname { sech } x d x = \sin ^ { - 1 } \left( 1 - x ^ { 2 } \right) + C\]
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Question

Quizplus · Accepted Answer

The integral of $2\operatorname{sech}x$ is actually $	an^{-1}\left(\sinh xight)+C$, not $\sin^{-1}\left(1-x^2ight)+C$. This can be verified by differentiating both sides to confirm that they yield the same integrand.

Verify the Integration Formula ∫2sech⁡xdx=sin⁡−1(1−x2)+C\int 2 \operatorname { sech } x d x = \sin ^ { - 1 } \left( 1 - x ^ { 2 } \right) + C∫2sechxdx=sin−1(1−x2)+C

Verify the Integration Formula $\int 2 \operatorname { sech } x d x = \sin ^ { - 1 } \left( 1 - x ^ { 2 } \right) + C$