Sr Examen
Integral de (2cosx+4sinx)/(2sinx-4cosx)^3 dx
Solución
Ha introducido
[src]
1 / | | 2*cos(x) + 4*sin(x) | ---------------------- dx | 3 | (2*sin(x) - 4*cos(x)) | / 0
$$\int\limits_{0}^{1} \frac{4 \sin{\left(x \right)} + 2 \cos{\left(x \right)}}{\left(2 \sin{\left(x \right)} - 4 \cos{\left(x \right)}\right)^{3}}\, dx$$
Integral((2*cos(x) + 4*sin(x))/(2*sin(x) - 4*cos(x))^3, (x, 0, 1))
Respuesta (Indefinida)
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/ 2/x\ 2/x\ /x\ 3/x\ | tan |-| 2*tan |-| 2*tan|-| 2*tan |-| | 2*cos(x) + 4*sin(x) \2/ \2/ \2/ \2/ | ---------------------- dx = C + ----------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------------- + ----------------------------------------------------- | 3 /x\ 2/x\ 4/x\ 3/x\ /x\ 2/x\ 4/x\ 3/x\ /x\ 2/x\ 4/x\ 3/x\ /x\ 2/x\ 4/x\ 3/x\ | (2*sin(x) - 4*cos(x)) 32 - 64*tan|-| - 32*tan |-| + 32*tan |-| + 64*tan |-| 16 - 32*tan|-| - 16*tan |-| + 16*tan |-| + 32*tan |-| 32 - 64*tan|-| - 32*tan |-| + 32*tan |-| + 64*tan |-| 32 - 64*tan|-| - 32*tan |-| + 32*tan |-| + 64*tan |-| | \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ /
$$\int \frac{4 \sin{\left(x \right)} + 2 \cos{\left(x \right)}}{\left(2 \sin{\left(x \right)} - 4 \cos{\left(x \right)}\right)^{3}}\, dx = C + \frac{2 \tan^{3}{\left(\frac{x}{2} \right)}}{32 \tan^{4}{\left(\frac{x}{2} \right)} + 64 \tan^{3}{\left(\frac{x}{2} \right)} - 32 \tan^{2}{\left(\frac{x}{2} \right)} - 64 \tan{\left(\frac{x}{2} \right)} + 32} + \frac{\tan^{2}{\left(\frac{x}{2} \right)}}{32 \tan^{4}{\left(\frac{x}{2} \right)} + 64 \tan^{3}{\left(\frac{x}{2} \right)} - 32 \tan^{2}{\left(\frac{x}{2} \right)} - 64 \tan{\left(\frac{x}{2} \right)} + 32} - \frac{2 \tan{\left(\frac{x}{2} \right)}}{32 \tan^{4}{\left(\frac{x}{2} \right)} + 64 \tan^{3}{\left(\frac{x}{2} \right)} - 32 \tan^{2}{\left(\frac{x}{2} \right)} - 64 \tan{\left(\frac{x}{2} \right)} + 32} - \frac{2 \tan^{2}{\left(\frac{x}{2} \right)}}{16 \tan^{4}{\left(\frac{x}{2} \right)} + 32 \tan^{3}{\left(\frac{x}{2} \right)} - 16 \tan^{2}{\left(\frac{x}{2} \right)} - 32 \tan{\left(\frac{x}{2} \right)} + 16}$$
Gráfica
Respuesta
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1 1
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32 2 2
8*sin (1) + 32*cos (1) - 32*cos(1)*sin(1)
$$\frac{1}{32} - \frac{1}{- 32 \sin{\left(1 \right)} \cos{\left(1 \right)} + 8 \sin^{2}{\left(1 \right)} + 32 \cos^{2}{\left(1 \right)}}$$
=
=
1 1
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32 2 2
8*sin (1) + 32*cos (1) - 32*cos(1)*sin(1)
$$\frac{1}{32} - \frac{1}{- 32 \sin{\left(1 \right)} \cos{\left(1 \right)} + 8 \sin^{2}{\left(1 \right)} + 32 \cos^{2}{\left(1 \right)}}$$
1/32 - 1/(8*sin(1)^2 + 32*cos(1)^2 - 32*cos(1)*sin(1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.