Sr Examen
Integral de cos^3(x)*cos(3*x) dx
Solución
Ha introducido
[src]
8/5 / | | 3 | cos (x)*cos(3*x) dx | / 0
$$\int\limits_{0}^{\frac{8}{5}} \cos^{3}{\left(x \right)} \cos{\left(3 x \right)}\, dx$$
Integral(cos(x)^3*cos(3*x), (x, 0, 8/5))
Respuesta (Indefinida)
[src]
/ | 3 | 3 sin (2*x) sin(2*x) x 3*sin(4*x) | cos (x)*cos(3*x) dx = C - --------- + -------- + - + ---------- | 12 4 8 32 /
$$\int \cos^{3}{\left(x \right)} \cos{\left(3 x \right)}\, dx = C + \frac{x}{8} - \frac{\sin^{3}{\left(2 x \right)}}{12} + \frac{\sin{\left(2 x \right)}}{4} + \frac{3 \sin{\left(4 x \right)}}{32}$$
Gráfica
Respuesta
[src]
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.