Sr Examen
Integral de X^2*cos(4x)^3 dx
Solución
Ha introducido
[src]
1 / | | 2 3 | x *cos (4*x) dx | / 0
$$\int\limits_{0}^{1} x^{2} \cos^{3}{\left(4 x \right)}\, dx$$
Integral(x^2*cos(4*x)^3, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | 3 2 2 3 3 2 2 2 | 2 3 5*sin (4*x) 7*cos (4*x)*sin(4*x) x *sin (4*x) 7*x*cos (4*x) x *cos (4*x)*sin(4*x) x*sin (4*x)*cos(4*x) | x *cos (4*x) dx = C - ----------- - -------------------- + ------------ + ------------- + --------------------- + -------------------- | 216 288 6 72 4 12 /
$$\int x^{2} \cos^{3}{\left(4 x \right)}\, dx = C + \frac{x^{2} \sin^{3}{\left(4 x \right)}}{6} + \frac{x^{2} \sin{\left(4 x \right)} \cos^{2}{\left(4 x \right)}}{4} + \frac{x \sin^{2}{\left(4 x \right)} \cos{\left(4 x \right)}}{12} + \frac{7 x \cos^{3}{\left(4 x \right)}}{72} - \frac{5 \sin^{3}{\left(4 x \right)}}{216} - \frac{7 \sin{\left(4 x \right)} \cos^{2}{\left(4 x \right)}}{288}$$
Gráfica
Respuesta
[src]
3 3 2 2
7*cos (4) 31*sin (4) sin (4)*cos(4) 65*cos (4)*sin(4)
--------- + ---------- + -------------- + -----------------
72 216 12 288
$$\frac{65 \sin{\left(4 \right)} \cos^{2}{\left(4 \right)}}{288} + \frac{31 \sin^{3}{\left(4 \right)}}{216} + \frac{\sin^{2}{\left(4 \right)} \cos{\left(4 \right)}}{12} + \frac{7 \cos^{3}{\left(4 \right)}}{72}$$
=
=
3 3 2 2
7*cos (4) 31*sin (4) sin (4)*cos(4) 65*cos (4)*sin(4)
--------- + ---------- + -------------- + -----------------
72 216 12 288
$$\frac{65 \sin{\left(4 \right)} \cos^{2}{\left(4 \right)}}{288} + \frac{31 \sin^{3}{\left(4 \right)}}{216} + \frac{\sin^{2}{\left(4 \right)} \cos{\left(4 \right)}}{12} + \frac{7 \cos^{3}{\left(4 \right)}}{72}$$
7*cos(4)^3/72 + 31*sin(4)^3/216 + sin(4)^2*cos(4)/12 + 65*cos(4)^2*sin(4)/288
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.