Sr Examen
Integral de ((2-tgx)^10)/((cosx)^2) dx
Solución
Ha introducido
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pi -- 4 / | | 10 | (2 - tan(x)) | -------------- dx | 2 | cos (x) | / 0
$$\int\limits_{0}^{\frac{\pi}{4}} \frac{\left(2 - \tan{\left(x \right)}\right)^{10}}{\cos^{2}{\left(x \right)}}\, dx$$
Integral((2 - tan(x))^10/cos(x)^2, (x, 0, pi/4))
Respuesta (Indefinida)
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/ | | 10 3 4 5 | (2 - tan(x)) 4 2560 / 2 \ / 2 \ / 2 \ 2 6469*sin(x) 1931*sin(x) sin(x) 215*sin(x) 4410*sin(x) 15038*sin(x) | -------------- dx = C - 3840*sec (x) - ------- - 1344*\-1 + sec (x)/ - 120*\-1 + sec (x)/ - 2*\-1 + sec (x)/ + 7680*sec (x) - ----------- - ----------- + ----------- + ---------- + ----------- + ------------ | 2 2 11*cos(x) 3 11 9 7 5 | cos (x) cos (x) 11*cos (x) 11*cos (x) 11*cos (x) 11*cos (x) 11*cos (x) | /
$$\int \frac{\left(2 - \tan{\left(x \right)}\right)^{10}}{\cos^{2}{\left(x \right)}}\, dx = C - 2 \left(\sec^{2}{\left(x \right)} - 1\right)^{5} - 120 \left(\sec^{2}{\left(x \right)} - 1\right)^{4} - 1344 \left(\sec^{2}{\left(x \right)} - 1\right)^{3} - \frac{6469 \sin{\left(x \right)}}{11 \cos{\left(x \right)}} - \frac{1931 \sin{\left(x \right)}}{11 \cos^{3}{\left(x \right)}} + \frac{15038 \sin{\left(x \right)}}{11 \cos^{5}{\left(x \right)}} + \frac{4410 \sin{\left(x \right)}}{11 \cos^{7}{\left(x \right)}} + \frac{215 \sin{\left(x \right)}}{11 \cos^{9}{\left(x \right)}} + \frac{\sin{\left(x \right)}}{11 \cos^{11}{\left(x \right)}} - 3840 \sec^{4}{\left(x \right)} + 7680 \sec^{2}{\left(x \right)} - \frac{2560}{\cos^{2}{\left(x \right)}}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.