Sr Examen
Integral de (sin^5)xcosx dx
Solución
Ha introducido
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1 / | | 5 | sin (x)*x*cos(x) dx | / 0
$$\int\limits_{0}^{1} x \sin^{5}{\left(x \right)} \cos{\left(x \right)}\, dx$$
Integral((sin(x)^5*x)*cos(x), (x, 0, 1))
Respuesta (Indefinida)
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/ | 6 3 3 5 6 5 2 4 4 2 | 5 5*x*cos (x) 5*cos (x)*sin (x) 5*cos (x)*sin(x) 11*x*sin (x) 11*sin (x)*cos(x) 5*x*cos (x)*sin (x) 5*x*cos (x)*sin (x) | sin (x)*x*cos(x) dx = C - ----------- + ----------------- + ---------------- + ------------ + ----------------- - ------------------- - ------------------- | 96 36 96 96 96 32 32 /
$$\int x \sin^{5}{\left(x \right)} \cos{\left(x \right)}\, dx = C + \frac{11 x \sin^{6}{\left(x \right)}}{96} - \frac{5 x \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)}}{32} - \frac{5 x \sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)}}{32} - \frac{5 x \cos^{6}{\left(x \right)}}{96} + \frac{11 \sin^{5}{\left(x \right)} \cos{\left(x \right)}}{96} + \frac{5 \sin^{3}{\left(x \right)} \cos^{3}{\left(x \right)}}{36} + \frac{5 \sin{\left(x \right)} \cos^{5}{\left(x \right)}}{96}$$
Gráfica
Respuesta
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6 6 2 4 4 2 3 3 5 5
5*cos (1) 11*sin (1) 5*cos (1)*sin (1) 5*cos (1)*sin (1) 5*cos (1)*sin (1) 5*cos (1)*sin(1) 11*sin (1)*cos(1)
- --------- + ---------- - ----------------- - ----------------- + ----------------- + ---------------- + -----------------
96 96 32 32 36 96 96
$$- \frac{5 \sin^{4}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{32} - \frac{5 \sin^{2}{\left(1 \right)} \cos^{4}{\left(1 \right)}}{32} - \frac{5 \cos^{6}{\left(1 \right)}}{96} + \frac{5 \sin{\left(1 \right)} \cos^{5}{\left(1 \right)}}{96} + \frac{5 \sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{36} + \frac{11 \sin^{5}{\left(1 \right)} \cos{\left(1 \right)}}{96} + \frac{11 \sin^{6}{\left(1 \right)}}{96}$$
=
=
6 6 2 4 4 2 3 3 5 5
5*cos (1) 11*sin (1) 5*cos (1)*sin (1) 5*cos (1)*sin (1) 5*cos (1)*sin (1) 5*cos (1)*sin(1) 11*sin (1)*cos(1)
- --------- + ---------- - ----------------- - ----------------- + ----------------- + ---------------- + -----------------
96 96 32 32 36 96 96
$$- \frac{5 \sin^{4}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{32} - \frac{5 \sin^{2}{\left(1 \right)} \cos^{4}{\left(1 \right)}}{32} - \frac{5 \cos^{6}{\left(1 \right)}}{96} + \frac{5 \sin{\left(1 \right)} \cos^{5}{\left(1 \right)}}{96} + \frac{5 \sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{36} + \frac{11 \sin^{5}{\left(1 \right)} \cos{\left(1 \right)}}{96} + \frac{11 \sin^{6}{\left(1 \right)}}{96}$$
-5*cos(1)^6/96 + 11*sin(1)^6/96 - 5*cos(1)^2*sin(1)^4/32 - 5*cos(1)^4*sin(1)^2/32 + 5*cos(1)^3*sin(1)^3/36 + 5*cos(1)^5*sin(1)/96 + 11*sin(1)^5*cos(1)/96
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.