Integral de (2^4*sin^6(x)*cos^2(x)) dx
Solución
Respuesta (Indefinida)
[src]
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| 3 5 5 3 7 8 8 7 2 6 6 2 4 4
| 6 2 73*cos (x)*sin (x) 55*cos (x)*sin (x) 5*cos (x)*sin(x) 5*x*cos (x) 5*x*sin (x) 5*sin (x)*cos(x) 5*x*cos (x)*sin (x) 5*x*cos (x)*sin (x) 15*x*cos (x)*sin (x)
| 16*sin (x)*cos (x) dx = C - ------------------ - ------------------ - ---------------- + ----------- + ----------- + ---------------- + ------------------- + ------------------- + --------------------
| 24 24 8 8 8 8 2 2 4
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$$\int 16 \sin^{6}{\left(x \right)} \cos^{2}{\left(x \right)}\, dx = C + \frac{5 x \sin^{8}{\left(x \right)}}{8} + \frac{5 x \sin^{6}{\left(x \right)} \cos^{2}{\left(x \right)}}{2} + \frac{15 x \sin^{4}{\left(x \right)} \cos^{4}{\left(x \right)}}{4} + \frac{5 x \sin^{2}{\left(x \right)} \cos^{6}{\left(x \right)}}{2} + \frac{5 x \cos^{8}{\left(x \right)}}{8} + \frac{5 \sin^{7}{\left(x \right)} \cos{\left(x \right)}}{8} - \frac{73 \sin^{5}{\left(x \right)} \cos^{3}{\left(x \right)}}{24} - \frac{55 \sin^{3}{\left(x \right)} \cos^{5}{\left(x \right)}}{24} - \frac{5 \sin{\left(x \right)} \cos^{7}{\left(x \right)}}{8}$$
$$\frac{5 \pi}{8}$$
=
$$\frac{5 \pi}{8}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.