Sr Examen
Integral de cosx^5cosx dx
Solución
Ha introducido
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1 / | | 5 | cos (x)*cos(x) dx | / 0
$$\int\limits_{0}^{1} \cos{\left(x \right)} \cos^{5}{\left(x \right)}\, dx$$
Integral(cos(x)^5*cos(x), (x, 0, 1))
Respuesta (Indefinida)
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/ | 5 3 | 5 5*x cos (x)*sin(x) 5*cos(x)*sin(x) 5*cos (x)*sin(x) | cos (x)*cos(x) dx = C + --- + -------------- + --------------- + ---------------- | 16 6 16 24 /
$$\int \cos{\left(x \right)} \cos^{5}{\left(x \right)}\, dx = C + \frac{5 x}{16} + \frac{\sin{\left(x \right)} \cos^{5}{\left(x \right)}}{6} + \frac{5 \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{24} + \frac{5 \sin{\left(x \right)} \cos{\left(x \right)}}{16}$$
Gráfica
Respuesta
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5 3 5 cos (1)*sin(1) 5*cos(1)*sin(1) 5*cos (1)*sin(1) -- + -------------- + --------------- + ---------------- 16 6 16 24
$$\frac{\sin{\left(1 \right)} \cos^{5}{\left(1 \right)}}{6} + \frac{5 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{24} + \frac{5 \sin{\left(1 \right)} \cos{\left(1 \right)}}{16} + \frac{5}{16}$$
=
=
5 3 5 cos (1)*sin(1) 5*cos(1)*sin(1) 5*cos (1)*sin(1) -- + -------------- + --------------- + ---------------- 16 6 16 24
$$\frac{\sin{\left(1 \right)} \cos^{5}{\left(1 \right)}}{6} + \frac{5 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{24} + \frac{5 \sin{\left(1 \right)} \cos{\left(1 \right)}}{16} + \frac{5}{16}$$
5/16 + cos(1)^5*sin(1)/6 + 5*cos(1)*sin(1)/16 + 5*cos(1)^3*sin(1)/24
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.