Sr Examen
Integral de sin2x*sinx*cos3x dx
Solución
Ha introducido
[src]
1 / | | sin(2*x)*sin(x)*cos(3*x) dx | / 0
$$\int\limits_{0}^{1} \sin{\left(x \right)} \sin{\left(2 x \right)} \cos{\left(3 x \right)}\, dx$$
Integral((sin(2*x)*sin(x))*cos(3*x), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ 3 | x sin (2*x) sin(4*x) | sin(2*x)*sin(x)*cos(3*x) dx = C - - + --------- + -------- | 4 6 16 /
$$\int \sin{\left(x \right)} \sin{\left(2 x \right)} \cos{\left(3 x \right)}\, dx = C - \frac{x}{4} + \frac{\sin^{3}{\left(2 x \right)}}{6} + \frac{\sin{\left(4 x \right)}}{16}$$
Gráfica
Respuesta
[src]
cos(1)*cos(2)*cos(3) cos(1)*sin(2)*sin(3) cos(2)*sin(1)*sin(3) cos(1)*cos(3)*sin(2) cos(3)*sin(1)*sin(2) cos(1)*cos(2)*sin(3) 5*sin(1)*sin(2)*sin(3)
- -------------------- - -------------------- - -------------------- - -------------------- + -------------------- + -------------------- + ----------------------
4 4 4 8 4 6 24
$$\frac{\sin{\left(1 \right)} \sin{\left(2 \right)} \cos{\left(3 \right)}}{4} - \frac{\cos{\left(1 \right)} \cos{\left(2 \right)} \cos{\left(3 \right)}}{4} - \frac{\sin{\left(2 \right)} \sin{\left(3 \right)} \cos{\left(1 \right)}}{4} + \frac{\sin{\left(3 \right)} \cos{\left(1 \right)} \cos{\left(2 \right)}}{6} - \frac{\sin{\left(1 \right)} \sin{\left(3 \right)} \cos{\left(2 \right)}}{4} + \frac{5 \sin{\left(1 \right)} \sin{\left(2 \right)} \sin{\left(3 \right)}}{24} - \frac{\sin{\left(2 \right)} \cos{\left(1 \right)} \cos{\left(3 \right)}}{8}$$
=
=
cos(1)*cos(2)*cos(3) cos(1)*sin(2)*sin(3) cos(2)*sin(1)*sin(3) cos(1)*cos(3)*sin(2) cos(3)*sin(1)*sin(2) cos(1)*cos(2)*sin(3) 5*sin(1)*sin(2)*sin(3)
- -------------------- - -------------------- - -------------------- - -------------------- + -------------------- + -------------------- + ----------------------
4 4 4 8 4 6 24
$$\frac{\sin{\left(1 \right)} \sin{\left(2 \right)} \cos{\left(3 \right)}}{4} - \frac{\cos{\left(1 \right)} \cos{\left(2 \right)} \cos{\left(3 \right)}}{4} - \frac{\sin{\left(2 \right)} \sin{\left(3 \right)} \cos{\left(1 \right)}}{4} + \frac{\sin{\left(3 \right)} \cos{\left(1 \right)} \cos{\left(2 \right)}}{6} - \frac{\sin{\left(1 \right)} \sin{\left(3 \right)} \cos{\left(2 \right)}}{4} + \frac{5 \sin{\left(1 \right)} \sin{\left(2 \right)} \sin{\left(3 \right)}}{24} - \frac{\sin{\left(2 \right)} \cos{\left(1 \right)} \cos{\left(3 \right)}}{8}$$
-cos(1)*cos(2)*cos(3)/4 - cos(1)*sin(2)*sin(3)/4 - cos(2)*sin(1)*sin(3)/4 - cos(1)*cos(3)*sin(2)/8 + cos(3)*sin(1)*sin(2)/4 + cos(1)*cos(2)*sin(3)/6 + 5*sin(1)*sin(2)*sin(3)/24
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.