In Exercises evaluate the definite integral using the formulas from Theorem 5.20.

Data from in Theorem 5.20

Transcribed Image Text:

THEOREM 5.20 Differentiation and Integration Involving Inverse Hyperbolic Functions Let u be a differentiable function of x. d -[sinh ! u] dx d dx d dx [tanh-1 u] [sech-¹ u] 1 Sa² Suva du u² ± a² du a² − u² du = = = a² ± u² u' u² + 1 u' 1 - u² - u' ul. u² 1 a + u In 2a u a + √√√a² ± u² |u| a = = In(u + √√√u² ± a²) + C 1 - —— a - In d dx + C d dx [coshu] d dx u' u]=√²-1 [coth-¹u] [csch-¹ u] + C = = = u' 1 - u² - u' |u|√1 + u²