Вопрос
Select all expressions matching the value of indefinite integral int (c^x-c^-x)dx e^x+(1)/(e^x)+C e^x-e^-x+C e^x+e^-x+C (e^2x+1)/(e^x)+C
Решения
4.7
(268 Голоса)
Федосей
Экспертная проверка
профессионал · Репетитор 6 лет
Ответ
To find the indefinite integral
, we can use the properties of exponential functions and integration.The correct answer is:
Explanation:The integral
can be rewritten as
.Using the properties of exponential functions, we know that
, where
is the hyperbolic sine function.Integrating
with respect to
gives
, where
is the hyperbolic cosine function.Since
, we can rewrite the integral as
.Therefore, the correct answer is
.