Предмет: Алгебра, автор: Аноним

Помогите пожалуйста решить задачу

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Автор ответа: Аноним

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Ответ:

На фото

Объяснение:

обведена замена

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Автор ответа: NNNLLL54

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Ответ:

Применяем метод замены переменной .

$\displaystyle 3)\ \ \int \frac{cosx\, dx}{4-sin^2x}=\Big[\ t=sinx\ ,\ dt=cosx\, dx\ \Bug]=\int \frac{dt}{2^2-t^2}=$

$\displaystyle =\frac{1}{2\cdot 2}\cdot ln\Big|\, \frac{2+t}{2-t}\, \Big|+C=\frac{1}{4}\cdot ln\Big|\, \frac{2+sinx}{2-sinx}\, \Big|+C$

$\displaystyle 4)\ \ \int \frac{1+\sqrt{ctgx}}{sin^2x}\, dx=\int \frac{dx}{sin^2x}+\int \frac{\sqrt{ctgx}}{sin^2x}\, dx=\Big[\ t=ctgx\ ,\ dt=-\frac{dx}{sinx^2x}\, \Big]=\\\\\\=-ctgx-\int \sqrt{t}\, dt=-ctgx-\frac{2\, t^{\frac{3}{2}}}{3} +C=-ctgx-\frac{2}{3}\, \sqrt{ctg^3x}+C$

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