Ответ:
[tex] \int^{ \frac{\pi}{4} } _{0} \frac{adx}{ \cos^{2} (bx + c) } = (\frac{a \tg(bx + c) }{b})| ^{ \frac{\pi}{4} } _{0}[/tex]
Подставляем значения:
[tex] (\frac{5 \tg(4x + 2)}{4} )| ^{ \frac{\pi}{4} } _{0} = \frac{5 \tg(4 \times \frac{\pi}{4} + 2 )}{4} - \frac{5 \tg(4 \times 0 + 2)}{4} = \frac{5 \tg(\pi + 2)}{4} - \frac{5 \tan(2) }{4} [/tex]
tg(π+α)=tg(α)
[tex] \frac{5 \tan(2) }{4} - \frac{5 \tan(2) }{4} = 0[/tex]
