Sr Examen
Integral de 2^4*sin^6(x)cos^2x dx
Solución
Ha introducido
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x / | | 6 2 | 16*sin (x)*cos (x) dx | / 0
$$\int\limits_{0}^{x} 16 \sin^{6}{\left(x \right)} \cos^{2}{\left(x \right)}\, dx$$
Integral((16*sin(x)^6)*cos(x)^2, (x, 0, x))
Respuesta (Indefinida)
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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 /
$$\int 16 \sin^{6}{\left(x \right)} \cos^{2}{\left(x \right)}\, dx = C + \frac{5 x \sin^{8}{\left(x \right)}}{8} + \frac{5 x \sin^{6}{\left(x \right)} \cos^{2}{\left(x \right)}}{2} + \frac{15 x \sin^{4}{\left(x \right)} \cos^{4}{\left(x \right)}}{4} + \frac{5 x \sin^{2}{\left(x \right)} \cos^{6}{\left(x \right)}}{2} + \frac{5 x \cos^{8}{\left(x \right)}}{8} + \frac{5 \sin^{7}{\left(x \right)} \cos{\left(x \right)}}{8} - \frac{73 \sin^{5}{\left(x \right)} \cos^{3}{\left(x \right)}}{24} - \frac{55 \sin^{3}{\left(x \right)} \cos^{5}{\left(x \right)}}{24} - \frac{5 \sin{\left(x \right)} \cos^{7}{\left(x \right)}}{8}$$
Respuesta
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3 5 5*x 7 5*cos(x)*sin(x) 5*sin (x)*cos(x) sin (x)*cos(x) --- + 2*sin (x)*cos(x) - --------------- - ---------------- - -------------- 8 8 12 3
$$\frac{5 x}{8} + 2 \sin^{7}{\left(x \right)} \cos{\left(x \right)} - \frac{\sin^{5}{\left(x \right)} \cos{\left(x \right)}}{3} - \frac{5 \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{12} - \frac{5 \sin{\left(x \right)} \cos{\left(x \right)}}{8}$$
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3 5 5*x 7 5*cos(x)*sin(x) 5*sin (x)*cos(x) sin (x)*cos(x) --- + 2*sin (x)*cos(x) - --------------- - ---------------- - -------------- 8 8 12 3
$$\frac{5 x}{8} + 2 \sin^{7}{\left(x \right)} \cos{\left(x \right)} - \frac{\sin^{5}{\left(x \right)} \cos{\left(x \right)}}{3} - \frac{5 \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{12} - \frac{5 \sin{\left(x \right)} \cos{\left(x \right)}}{8}$$
5*x/8 + 2*sin(x)^7*cos(x) - 5*cos(x)*sin(x)/8 - 5*sin(x)^3*cos(x)/12 - sin(x)^5*cos(x)/3
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.