15 БАЛЛОВ! Решите интеграл: dx/((2x+3)^4). Created by Chamomiilee. algebra-ru

((2x+3)^4)...

Chamomiilee @Chamomiilee

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15 БАЛЛОВ! Решите интеграл: dx/((2x+3)^4)

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$\int \frac{dx}{(2x+3)^4}=\int (2x+3)^{-4}dx=[t=2x+3\; ,\; dt=2dx\; ,\; dx=\frac{dt}{2}]=\\\\=\frac{1}{2}\cdot \int t^{-4}\cdot dt=\frac{1}{2}\cdot \frac{t^{-3}}{-3}+C=\frac{1}{2}\cdot \frac{(2x+3)^{-3}}{-3}+C=-\frac{1}{6(2x+3)^3}+C$

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python 80 ballov reshit s pomoshyu ciklov diapazonov 1napishite programmu kot

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