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
4.7268 голоса
Федосей
профессионал · Репетитор 6 летЭкспертная проверка
Отвечать
To find the indefinite integral $\int (c^{c^{-x})dx, we can use the properties of exponential functions and integration. The correct answer is: e^{x}+e^{-x}+C Explanation: The integral \int (c^{x}-c^{-x})dx can be rewritten as \int (e^{x}-e^{-x})dx. Using the properties of exponential functions, we know that e^{x} - e^{-x} = 2\sinh(x), where \sinh(x) is the hyperbolic sine function. Integrating 2\sinh(x) with respect to x gives 2\cosh(x) + C, where \cosh(x) is the hyperbolic cosine function. Since \cosh(x) = \frac{e^{x}^{-x}}{2}, we can rewrite the integral as \int (e^{x} - e^{-x})dx = 2\cosh(x) + C = e^{x} + e^{-x} + C. Therefore, the correct answer is e^{x} + e^{-x} + C$.
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