Integral de Cos^3x*cos3x dx
Solución
Respuesta (Indefinida)
[src]
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| 3
| 3 sin (2*x) sin(2*x) x 3*sin(4*x)
| cos (x)*cos(3*x) dx = C - --------- + -------- + - + ----------
| 12 4 8 32
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$$\int \cos^{3}{\left(x \right)} \cos{\left(3 x \right)}\, dx = C + \frac{x}{8} - \frac{\sin^{3}{\left(2 x \right)}}{12} + \frac{\sin{\left(2 x \right)}}{4} + \frac{3 \sin{\left(4 x \right)}}{32}$$
3 3 3 3 2 2 2
sin (8/5)*sin(24/5) sin (8/5)*cos(24/5) cos (8/5)*cos(24/5) 3*cos (8/5)*sin(24/5) 3*sin (8/5)*cos(8/5)*cos(24/5) cos (8/5)*cos(24/5)*sin(8/5) 3*cos (8/5)*sin(8/5)*sin(24/5)
- ------------------- - ------------------- + ------------------- + --------------------- - ------------------------------ - ---------------------------- + ------------------------------
5 24 5 8 5 4 5
$$- \frac{\sin^{3}{\left(\frac{8}{5} \right)} \cos{\left(\frac{24}{5} \right)}}{24} + \frac{3 \sin{\left(\frac{8}{5} \right)} \sin{\left(\frac{24}{5} \right)} \cos^{2}{\left(\frac{8}{5} \right)}}{5} - \frac{\sin{\left(\frac{8}{5} \right)} \cos^{2}{\left(\frac{8}{5} \right)} \cos{\left(\frac{24}{5} \right)}}{4} + \frac{\cos^{3}{\left(\frac{8}{5} \right)} \cos{\left(\frac{24}{5} \right)}}{5} + \frac{3 \sin{\left(\frac{24}{5} \right)} \cos^{3}{\left(\frac{8}{5} \right)}}{8} - \frac{3 \sin^{2}{\left(\frac{8}{5} \right)} \cos{\left(\frac{8}{5} \right)} \cos{\left(\frac{24}{5} \right)}}{5} - \frac{\sin^{3}{\left(\frac{8}{5} \right)} \sin{\left(\frac{24}{5} \right)}}{5}$$
=
3 3 3 3 2 2 2
sin (8/5)*sin(24/5) sin (8/5)*cos(24/5) cos (8/5)*cos(24/5) 3*cos (8/5)*sin(24/5) 3*sin (8/5)*cos(8/5)*cos(24/5) cos (8/5)*cos(24/5)*sin(8/5) 3*cos (8/5)*sin(8/5)*sin(24/5)
- ------------------- - ------------------- + ------------------- + --------------------- - ------------------------------ - ---------------------------- + ------------------------------
5 24 5 8 5 4 5
$$- \frac{\sin^{3}{\left(\frac{8}{5} \right)} \cos{\left(\frac{24}{5} \right)}}{24} + \frac{3 \sin{\left(\frac{8}{5} \right)} \sin{\left(\frac{24}{5} \right)} \cos^{2}{\left(\frac{8}{5} \right)}}{5} - \frac{\sin{\left(\frac{8}{5} \right)} \cos^{2}{\left(\frac{8}{5} \right)} \cos{\left(\frac{24}{5} \right)}}{4} + \frac{\cos^{3}{\left(\frac{8}{5} \right)} \cos{\left(\frac{24}{5} \right)}}{5} + \frac{3 \sin{\left(\frac{24}{5} \right)} \cos^{3}{\left(\frac{8}{5} \right)}}{8} - \frac{3 \sin^{2}{\left(\frac{8}{5} \right)} \cos{\left(\frac{8}{5} \right)} \cos{\left(\frac{24}{5} \right)}}{5} - \frac{\sin^{3}{\left(\frac{8}{5} \right)} \sin{\left(\frac{24}{5} \right)}}{5}$$
-sin(8/5)^3*sin(24/5)/5 - sin(8/5)^3*cos(24/5)/24 + cos(8/5)^3*cos(24/5)/5 + 3*cos(8/5)^3*sin(24/5)/8 - 3*sin(8/5)^2*cos(8/5)*cos(24/5)/5 - cos(8/5)^2*cos(24/5)*sin(8/5)/4 + 3*cos(8/5)^2*sin(8/5)*sin(24/5)/5
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.