Помогите решить интеграл: [tex]\int\limits {\frac{1-tgx}{1+tgx} } \, dx[/tex] Ответ: [tex]ln|sinx+cosx|+ C[/tex]. Created by milakamilat1m. matematika-ru

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Ответ:

$\displaystyle \int \frac{1-tgx}{1+tgx}\, dx=\int \frac{1-\frac{sinx}{cosx}}{1+\frac{sinx}{cosx}}=\int \frac{cosx-sinx}{cosx+sinx}\, dx=\Big[\ t=cosx+sinx\ ,\\\\\\dt=(-sinx+cosx)\, dx\ \Big]=\int \frac{dt}{t}=ln|t|+C=ln|cosx+sinx|+C\ ;$

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