Sr Examen
Integral de 〖cos〗^3x*sinx dx
Solución
Ha introducido
[src]
1 / | | 3 | cos (x)*x*sin(x) dx | / 0
$$\int\limits_{0}^{1} x \cos^{3}{\left(x \right)} \sin{\left(x \right)}\, dx$$
Integral((cos(x)^3*x)*sin(x), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | 4 4 3 3 2 2 | 3 5*x*cos (x) 3*x*sin (x) 3*sin (x)*cos(x) 5*cos (x)*sin(x) 3*x*cos (x)*sin (x) | cos (x)*x*sin(x) dx = C - ----------- + ----------- + ---------------- + ---------------- + ------------------- | 32 32 32 32 16 /
$$\int x \cos^{3}{\left(x \right)} \sin{\left(x \right)}\, dx = C + \frac{3 x \sin^{4}{\left(x \right)}}{32} + \frac{3 x \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{16} - \frac{5 x \cos^{4}{\left(x \right)}}{32} + \frac{3 \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{32} + \frac{5 \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{32}$$
Gráfica
Respuesta
[src]
4 4 2 2 3 3
5*cos (1) 3*sin (1) 3*cos (1)*sin (1) 3*sin (1)*cos(1) 5*cos (1)*sin(1)
- --------- + --------- + ----------------- + ---------------- + ----------------
32 32 16 32 32
$$- \frac{5 \cos^{4}{\left(1 \right)}}{32} + \frac{5 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{32} + \frac{3 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{32} + \frac{3 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{16} + \frac{3 \sin^{4}{\left(1 \right)}}{32}$$
=
=
4 4 2 2 3 3
5*cos (1) 3*sin (1) 3*cos (1)*sin (1) 3*sin (1)*cos(1) 5*cos (1)*sin(1)
- --------- + --------- + ----------------- + ---------------- + ----------------
32 32 16 32 32
$$- \frac{5 \cos^{4}{\left(1 \right)}}{32} + \frac{5 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{32} + \frac{3 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{32} + \frac{3 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{16} + \frac{3 \sin^{4}{\left(1 \right)}}{32}$$
-5*cos(1)^4/32 + 3*sin(1)^4/32 + 3*cos(1)^2*sin(1)^2/16 + 3*sin(1)^3*cos(1)/32 + 5*cos(1)^3*sin(1)/32
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.