Предмет: Математика, автор: lyovademyanov

задание по матанализу

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Автор ответа: Alnadya

0

Решение.

Решаем методом подстановки .

$\bf \displaystyle 1.\ \int \frac{x^2\, dx}{1+x^3}=\Big[\ u=1+x^3\ ,\ du=3x^2\, dx\ \Big]=\frac{1}{3}\int \frac{du}{u}=\frac{1}{3}\cdot ln|\, u\, |+C=\\\\\\=\frac{1}{3}\cdot ln|\, 1+x^3\, |+C$

$\bf \displaystyle 2.\ \int \frac{3\, dx}{cos^22x}=\Big[\ u=2x\ ,\ du=2\, dx\ \Big]=\frac{3}{2}\int \frac{du}{cos^2u}=\frac{3}{2}\cdot tg\, u+C=\\\\\\=\frac{3}{2}\cdot tg\, 2x+C$

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