Sr Examen
Integral de 2*sin^2(x)/cos^2(x-1) dx
Solución
Ha introducido
[src]
6 / | | 2 | 2*sin (x) | ----------- dx | 2 | cos (x - 1) | / -5
$$\int\limits_{-5}^{6} \frac{2 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x - 1 \right)}}\, dx$$
Integral((2*sin(x)^2)/cos(x - 1)^2, (x, -5, 6))
Respuesta (Indefinida)
[src]
/ | | 2 4 2 2 4 2 2 3 2 2 3 3 | 2*sin (x) 2*cos (1)*cos(x) 2*cos (1)*sin (1)*cos(x) 2*x*sin (1)*sin(x) 4*cos (1)*sin (1)*cos(x)*log(cos(1)*cos(x) + sin(1)*sin(x)) 4*sin (1)*cos(1)*log(cos(1)*cos(x) + sin(1)*sin(x))*sin(x) 2*x*cos (1)*sin (1)*sin(x) 2*x*cos (1)*cos(x)*sin(1) 2*x*sin (1)*cos(1)*cos(x) | ----------- dx = C - --------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------- | 2 6 4 2 5 5 2 4 3 3 6 4 2 5 5 2 4 3 3 6 4 2 5 5 2 4 3 3 6 4 2 5 5 2 4 3 3 6 4 2 5 5 2 4 3 3 6 4 2 5 5 2 4 3 3 6 4 2 5 5 2 4 3 3 6 4 2 5 5 2 4 3 3 | cos (x - 1) sin (1)*sin(x) + cos (1)*sin (1)*sin(x) + cos (1)*cos(x)*sin(1) + sin (1)*cos(1)*cos(x) + 2*cos (1)*sin (1)*sin(x) + 2*cos (1)*sin (1)*cos(x) sin (1)*sin(x) + cos (1)*sin (1)*sin(x) + cos (1)*cos(x)*sin(1) + sin (1)*cos(1)*cos(x) + 2*cos (1)*sin (1)*sin(x) + 2*cos (1)*sin (1)*cos(x) sin (1)*sin(x) + cos (1)*sin (1)*sin(x) + cos (1)*cos(x)*sin(1) + sin (1)*cos(1)*cos(x) + 2*cos (1)*sin (1)*sin(x) + 2*cos (1)*sin (1)*cos(x) sin (1)*sin(x) + cos (1)*sin (1)*sin(x) + cos (1)*cos(x)*sin(1) + sin (1)*cos(1)*cos(x) + 2*cos (1)*sin (1)*sin(x) + 2*cos (1)*sin (1)*cos(x) sin (1)*sin(x) + cos (1)*sin (1)*sin(x) + cos (1)*cos(x)*sin(1) + sin (1)*cos(1)*cos(x) + 2*cos (1)*sin (1)*sin(x) + 2*cos (1)*sin (1)*cos(x) sin (1)*sin(x) + cos (1)*sin (1)*sin(x) + cos (1)*cos(x)*sin(1) + sin (1)*cos(1)*cos(x) + 2*cos (1)*sin (1)*sin(x) + 2*cos (1)*sin (1)*cos(x) sin (1)*sin(x) + cos (1)*sin (1)*sin(x) + cos (1)*cos(x)*sin(1) + sin (1)*cos(1)*cos(x) + 2*cos (1)*sin (1)*sin(x) + 2*cos (1)*sin (1)*cos(x) sin (1)*sin(x) + cos (1)*sin (1)*sin(x) + cos (1)*cos(x)*sin(1) + sin (1)*cos(1)*cos(x) + 2*cos (1)*sin (1)*sin(x) + 2*cos (1)*sin (1)*cos(x) | /
$$\int \frac{2 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x - 1 \right)}}\, dx = C - \frac{2 x \sin^{2}{\left(1 \right)} \sin{\left(x \right)} \cos^{2}{\left(1 \right)}}{\sin^{2}{\left(1 \right)} \sin{\left(x \right)} \cos^{4}{\left(1 \right)} + 2 \sin^{4}{\left(1 \right)} \sin{\left(x \right)} \cos^{2}{\left(1 \right)} + \sin^{6}{\left(1 \right)} \sin{\left(x \right)} + \sin{\left(1 \right)} \cos^{5}{\left(1 \right)} \cos{\left(x \right)} + 2 \sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)} \cos{\left(x \right)} + \sin^{5}{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(x \right)}} + \frac{2 x \sin^{4}{\left(1 \right)} \sin{\left(x \right)}}{\sin^{2}{\left(1 \right)} \sin{\left(x \right)} \cos^{4}{\left(1 \right)} + 2 \sin^{4}{\left(1 \right)} \sin{\left(x \right)} \cos^{2}{\left(1 \right)} + \sin^{6}{\left(1 \right)} \sin{\left(x \right)} + \sin{\left(1 \right)} \cos^{5}{\left(1 \right)} \cos{\left(x \right)} + 2 \sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)} \cos{\left(x \right)} + \sin^{5}{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(x \right)}} - \frac{2 x \sin{\left(1 \right)} \cos^{3}{\left(1 \right)} \cos{\left(x \right)}}{\sin^{2}{\left(1 \right)} \sin{\left(x \right)} \cos^{4}{\left(1 \right)} + 2 \sin^{4}{\left(1 \right)} \sin{\left(x \right)} \cos^{2}{\left(1 \right)} + \sin^{6}{\left(1 \right)} \sin{\left(x \right)} + \sin{\left(1 \right)} \cos^{5}{\left(1 \right)} \cos{\left(x \right)} + 2 \sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)} \cos{\left(x \right)} + \sin^{5}{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(x \right)}} + \frac{2 x \sin^{3}{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(x \right)}}{\sin^{2}{\left(1 \right)} \sin{\left(x \right)} \cos^{4}{\left(1 \right)} + 2 \sin^{4}{\left(1 \right)} \sin{\left(x \right)} \cos^{2}{\left(1 \right)} + \sin^{6}{\left(1 \right)} \sin{\left(x \right)} + \sin{\left(1 \right)} \cos^{5}{\left(1 \right)} \cos{\left(x \right)} + 2 \sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)} \cos{\left(x \right)} + \sin^{5}{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(x \right)}} - \frac{4 \log{\left(\sin{\left(1 \right)} \sin{\left(x \right)} + \cos{\left(1 \right)} \cos{\left(x \right)} \right)} \sin^{3}{\left(1 \right)} \sin{\left(x \right)} \cos{\left(1 \right)}}{\sin^{2}{\left(1 \right)} \sin{\left(x \right)} \cos^{4}{\left(1 \right)} + 2 \sin^{4}{\left(1 \right)} \sin{\left(x \right)} \cos^{2}{\left(1 \right)} + \sin^{6}{\left(1 \right)} \sin{\left(x \right)} + \sin{\left(1 \right)} \cos^{5}{\left(1 \right)} \cos{\left(x \right)} + 2 \sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)} \cos{\left(x \right)} + \sin^{5}{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(x \right)}} - \frac{4 \log{\left(\sin{\left(1 \right)} \sin{\left(x \right)} + \cos{\left(1 \right)} \cos{\left(x \right)} \right)} \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)} \cos{\left(x \right)}}{\sin^{2}{\left(1 \right)} \sin{\left(x \right)} \cos^{4}{\left(1 \right)} + 2 \sin^{4}{\left(1 \right)} \sin{\left(x \right)} \cos^{2}{\left(1 \right)} + \sin^{6}{\left(1 \right)} \sin{\left(x \right)} + \sin{\left(1 \right)} \cos^{5}{\left(1 \right)} \cos{\left(x \right)} + 2 \sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)} \cos{\left(x \right)} + \sin^{5}{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(x \right)}} - \frac{2 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)} \cos{\left(x \right)}}{\sin^{2}{\left(1 \right)} \sin{\left(x \right)} \cos^{4}{\left(1 \right)} + 2 \sin^{4}{\left(1 \right)} \sin{\left(x \right)} \cos^{2}{\left(1 \right)} + \sin^{6}{\left(1 \right)} \sin{\left(x \right)} + \sin{\left(1 \right)} \cos^{5}{\left(1 \right)} \cos{\left(x \right)} + 2 \sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)} \cos{\left(x \right)} + \sin^{5}{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(x \right)}} - \frac{2 \cos^{4}{\left(1 \right)} \cos{\left(x \right)}}{\sin^{2}{\left(1 \right)} \sin{\left(x \right)} \cos^{4}{\left(1 \right)} + 2 \sin^{4}{\left(1 \right)} \sin{\left(x \right)} \cos^{2}{\left(1 \right)} + \sin^{6}{\left(1 \right)} \sin{\left(x \right)} + \sin{\left(1 \right)} \cos^{5}{\left(1 \right)} \cos{\left(x \right)} + 2 \sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)} \cos{\left(x \right)} + \sin^{5}{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(x \right)}}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.