∫ 0 π 1 − s e n ( x ) c o s ( x ) d x = {\displaystyle \int _{0}^{\pi }{\frac {1-sen(x)}{cos(x)}}dx=}
∫ 0 π 1 c o s ( x ) d x − ∫ 0 π s e n ( x ) c o s ( x ) d x = {\displaystyle \int _{0}^{\pi }{\frac {1}{cos(x)}}dx-\int _{0}^{\pi }{\frac {sen(x)}{cos(x)}}dx=}
∫ 0 π s e c ( x ) d x − ∫ 0 π t g ( x ) d x {\displaystyle \int _{0}^{\pi }sec(x)dx-\int _{0}^{\pi }tg(x)dx}
{ l n | ( t g ( x ) + s e c ( x ) | } 0 π − [ s e c 2 ( x ) ] 0 π = {\displaystyle \{ln|(tg(x)+sec(x)|\}_{0}^{\pi }-[sec^{2}(x)]_{0}^{\pi }=}
l n | t g ( π ) + s e c ( π ) | − l n | t g ( 0 ) + s e c ( 0 ) | − [ s e c 2 ( π ) − s e c 2 ( 0 ) ] = {\displaystyle ln|tg(\pi )+sec(\pi )|-ln|tg(0)+sec(0)|-[sec^{2}(\pi )-sec^{2}(0)]=}
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![{\displaystyle \{ln|(tg(x)+sec(x)|\}_{0}^{\pi }-[sec^{2}(x)]_{0}^{\pi }=}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6f1517557b1c6f39518b35a3baaef392fc88c0d4)
![{\displaystyle ln|tg(\pi )+sec(\pi )|-ln|tg(0)+sec(0)|-[sec^{2}(\pi )-sec^{2}(0)]=}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a2996a458d7deecf13d75c43bb051b25c329c19a)
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