Sr Examen
Integral de (sin(x))/(1+2cos(x))^4 dx
Solución
Ha introducido
[src]
x - 2 / | | sin(x) | --------------- dx | 4 | (1 + 2*cos(x)) | / 0
$$\int\limits_{0}^{\frac{x}{2}} \frac{\sin{\left(x \right)}}{\left(2 \cos{\left(x \right)} + 1\right)^{4}}\, dx$$
Integral(sin(x)/(1 + 2*cos(x))^4, (x, 0, x/2))
Respuesta (Indefinida)
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/ | | sin(x) 1 | --------------- dx = C + --------------------------------------- | 4 3 2 | (1 + 2*cos(x)) 6 + 36*cos(x) + 48*cos (x) + 72*cos (x) | /
$$\int \frac{\sin{\left(x \right)}}{\left(2 \cos{\left(x \right)} + 1\right)^{4}}\, dx = C + \frac{1}{48 \cos^{3}{\left(x \right)} + 72 \cos^{2}{\left(x \right)} + 36 \cos{\left(x \right)} + 6}$$
Respuesta
[src]
1 1
- --- + ---------------------------------------
162 /x\ 3/x\ 2/x\
6 + 36*cos|-| + 48*cos |-| + 72*cos |-|
\2/ \2/ \2/
$$- \frac{1}{162} + \frac{1}{48 \cos^{3}{\left(\frac{x}{2} \right)} + 72 \cos^{2}{\left(\frac{x}{2} \right)} + 36 \cos{\left(\frac{x}{2} \right)} + 6}$$
=
=
1 1
- --- + ---------------------------------------
162 /x\ 3/x\ 2/x\
6 + 36*cos|-| + 48*cos |-| + 72*cos |-|
\2/ \2/ \2/
$$- \frac{1}{162} + \frac{1}{48 \cos^{3}{\left(\frac{x}{2} \right)} + 72 \cos^{2}{\left(\frac{x}{2} \right)} + 36 \cos{\left(\frac{x}{2} \right)} + 6}$$
-1/162 + 1/(6 + 36*cos(x/2) + 48*cos(x/2)^3 + 72*cos(x/2)^2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.