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