Sr Examen
Integral de cos2(2x-12)dx dx
Solución
Ha introducido
[src]
1 / | | 2 | cos (2*x - 12) dx | / 0
$$\int\limits_{0}^{1} \cos^{2}{\left(2 x - 12 \right)}\, dx$$
Integral(cos(2*x - 12)^2, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | 3 4 2 | 2 x tan(-6 + x) tan (-6 + x) x*tan (-6 + x) 2*x*tan (-6 + x) | cos (2*x - 12) dx = C + ----------------------------------- + ----------------------------------- - ----------------------------------- + ----------------------------------- + ----------------------------------- | 4 2 4 2 4 2 4 2 4 2 / 2 + 2*tan (-6 + x) + 4*tan (-6 + x) 2 + 2*tan (-6 + x) + 4*tan (-6 + x) 2 + 2*tan (-6 + x) + 4*tan (-6 + x) 2 + 2*tan (-6 + x) + 4*tan (-6 + x) 2 + 2*tan (-6 + x) + 4*tan (-6 + x)
$$\int \cos^{2}{\left(2 x - 12 \right)}\, dx = C + \frac{x \tan^{4}{\left(x - 6 \right)}}{2 \tan^{4}{\left(x - 6 \right)} + 4 \tan^{2}{\left(x - 6 \right)} + 2} + \frac{2 x \tan^{2}{\left(x - 6 \right)}}{2 \tan^{4}{\left(x - 6 \right)} + 4 \tan^{2}{\left(x - 6 \right)} + 2} + \frac{x}{2 \tan^{4}{\left(x - 6 \right)} + 4 \tan^{2}{\left(x - 6 \right)} + 2} - \frac{\tan^{3}{\left(x - 6 \right)}}{2 \tan^{4}{\left(x - 6 \right)} + 4 \tan^{2}{\left(x - 6 \right)} + 2} + \frac{\tan{\left(x - 6 \right)}}{2 \tan^{4}{\left(x - 6 \right)} + 4 \tan^{2}{\left(x - 6 \right)} + 2}$$
Gráfica
Respuesta
[src]
2 2 cos (10) sin (10) cos(10)*sin(10) cos(12)*sin(12) -------- + -------- - --------------- + --------------- 2 2 4 4
$$- \frac{\sin{\left(10 \right)} \cos{\left(10 \right)}}{4} + \frac{\sin{\left(12 \right)} \cos{\left(12 \right)}}{4} + \frac{\sin^{2}{\left(10 \right)}}{2} + \frac{\cos^{2}{\left(10 \right)}}{2}$$
=
=
2 2 cos (10) sin (10) cos(10)*sin(10) cos(12)*sin(12) -------- + -------- - --------------- + --------------- 2 2 4 4
$$- \frac{\sin{\left(10 \right)} \cos{\left(10 \right)}}{4} + \frac{\sin{\left(12 \right)} \cos{\left(12 \right)}}{4} + \frac{\sin^{2}{\left(10 \right)}}{2} + \frac{\cos^{2}{\left(10 \right)}}{2}$$
cos(10)^2/2 + sin(10)^2/2 - cos(10)*sin(10)/4 + cos(12)*sin(12)/4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.