Lesson 8 - Integration of Hyperbolic Functions

# Lesson 8 - Integration of Hyperbolic Functions -...

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Integration of Hyperbolic Functions

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OBJECTIVES OBJECTIVES identify the different hyperbolic functions; find the integral of given hyperbolic functions; determine the difference between the integrals of hyperbolic functions; and evaluate integrals involving hyperbolic functions.
2 sinh . 1 x x e e x - - = 2 cosh . 2 x x e e x - + = x x x x e e e e x x x - - + - = = cosh sinh tanh . 3 x x x x e e e e x x - - - + = = tanh 1 coth . 4 x x e e x hx - + = = 2 cosh 1 sec . 5 x x e e x hx - - = = 2 sinh 1 csc . 6 Definitions:

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Differentiation Formulas ( 29 udu u d cosh sinh . 1 = ( 29 udu u d sinh cosh . 2 = ( 29 udu h u d 2 sec tanh . 3 = ( 29 udu h u d 2 csc coth . 4 - = ( 29 udu hu hu d tanh sec sec . 5 - = ( 29 udu coth hu csc hu csc d . 6 - =
. Note : The hyperbolic functions are defined in terms of the exponential functions. Its differentials may also be found by differentiating its equivalent exponential form. Similarly, the integrals of the hyperbolic functions can be derived by integrating the exponential form equivalent.

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Integration Formulas C u udu + = cosh sinh . 1 C u udu + = sinh cosh . 2
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