(a) Derive the identitysech2 x1 + tanh2 x = sech 2x(b) Use the result in part (a) to

Chapter 7, Problem 32

(choose chapter or problem)

(a) Derive the identity

$\frac{\operatorname{sech}^{2} x}{1+\tanh ^{2} x} \operatorname{sech} 2 x$

(b) Use the result in part (a) to evaluate $\int \operatorname{sech} x d x$.

$\operatorname{sech} x=\frac{2 e^{x}}{e^{2 x}+1}$

(d) Use the result in part (c) to evaluate $\int \operatorname{sech} x d x$.

(e) Explain why your answers to parts (b) and (d) are consistent.

Equation Transcription:

$\frac{sec{h}^{2}x}{1+tan{h}^{2}x}sech\ 2x$

$\int\limits_{\ }^{\ }sech\ x\ dx$

$sech\ x=\frac{2{e}^{x}}{{e}^{2x}+1}$

$\int\limits_{\ }^{\ }sech\ x\ dx$

Text Transcription:

sech^2 x/ 1+tanh^2 x sech 2x

Integral sech x dx

Sech x = 2e^x/e^2x+1

Integral sech x dx

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