Integral de ∫(sen^4)xcosxdx dx
Solución
Respuesta (Indefinida)
[src]
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| 5 5 4 3 2
| 4 8*cos (x) x*sin (x) sin (x)*cos(x) 4*cos (x)*sin (x)
| sin (x)*x*cos(x) dx = C + --------- + --------- + -------------- + -----------------
| 75 5 5 15
/
$$\int x \sin^{4}{\left(x \right)} \cos{\left(x \right)}\, dx = C + \frac{x \sin^{5}{\left(x \right)}}{5} + \frac{\sin^{4}{\left(x \right)} \cos{\left(x \right)}}{5} + \frac{4 \sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}}{15} + \frac{8 \cos^{5}{\left(x \right)}}{75}$$
5 5 4 3 2
8 sin (1) 8*cos (1) sin (1)*cos(1) 4*cos (1)*sin (1)
- -- + ------- + --------- + -------------- + -----------------
75 5 75 5 15
$$- \frac{8}{75} + \frac{8 \cos^{5}{\left(1 \right)}}{75} + \frac{4 \sin^{2}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{15} + \frac{\sin^{4}{\left(1 \right)} \cos{\left(1 \right)}}{5} + \frac{\sin^{5}{\left(1 \right)}}{5}$$
=
5 5 4 3 2
8 sin (1) 8*cos (1) sin (1)*cos(1) 4*cos (1)*sin (1)
- -- + ------- + --------- + -------------- + -----------------
75 5 75 5 15
$$- \frac{8}{75} + \frac{8 \cos^{5}{\left(1 \right)}}{75} + \frac{4 \sin^{2}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{15} + \frac{\sin^{4}{\left(1 \right)} \cos{\left(1 \right)}}{5} + \frac{\sin^{5}{\left(1 \right)}}{5}$$
-8/75 + sin(1)^5/5 + 8*cos(1)^5/75 + sin(1)^4*cos(1)/5 + 4*cos(1)^3*sin(1)^2/15
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.