Предмет: Математика, автор: evgeniamalaa23

помогите решить , хоть что то

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Ответы

Автор ответа: Alnadya

1

Пошаговое объяснение.

1) Табличные интегралы.

$\displaystyle \int \Big(tgx+\frac{1}{cos^2x}\Big)\, dx=\int tgx\, dx+\int \frac{dx}{cos^2x}=-ln|cosx|+tgx+C$

2) Метод замены переменных.

$\displaystyle a)\ \ \int x^2\, e^{x^3}\, dx=\Big[\ t=x^3\ ,\ dt=3x^2\, dx\ ,\ x^2\, dx=\frac{dt}{3}\ \Big]=\frac{1}{3}\int e^{t}\, dt=\\\\\\=\frac{1}{3}\, e^{t}+C=\frac{1}{3}\, e^{x^3}+C\\\\b)\ \ \int \frac{1-2cosx}{sin^2x}\, dx=\int \frac{dx}{sin^2x}-2\int \frac{cosx\, dx}{sin^2x}=\Big[\ t=sinx\ ,\ dt=cosx\, dx\ \Big]=\\\\\\=-ctgx-2\int \frac{dt}{t^2}=-ctgx-2\int t^{-2}\, dt=-ctgx-2\cdot \frac{t^{-1}}{-1}+C=\\\\\\=-ctgx+\frac{2}{sinx}+C$

evgeniamalaa23: спасибо большое

Alnadya: пожалуйста

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