Вычисли интеграл, сделав подходящую замену. Created by RoadGoodGame. matematika-ru

Вычисли интеграл, сделав подходящую замену...

RoadGoodGame @RoadGoodGame

November 2021 1 31 Report

Вычисли интеграл, сделав подходящую замену

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Miroslava227

Ответ:

$\sin(x - 7) = t \\ \cos(x - 7) dx = dt$

$\int\limits\frac{dt}{49 + {t}^{2} } = \int\limits \frac{dt}{ {t}^{2} + {7}^{2} } = \\ = \frac{1}{7} arcrtg( \frac{t}{7} ) + C = \frac{1}{7} arctg( \frac{ \sin(x - 7) }{7} ) + C$

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