Sr Examen
Integral de sinx/(1+sinx) dx
Solución
Ha introducido
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1 / | | sin(x) | ---------- dx | 1 + sin(x) | / 0
$$\int\limits_{0}^{1} \frac{\sin{\left(x \right)}}{\sin{\left(x \right)} + 1}\, dx$$
Integral(sin(x)/(1 + sin(x)), (x, 0, 1))
Respuesta (Indefinida)
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/ /x\ | x*tan|-| | sin(x) 2 x \2/ | ---------- dx = C + ---------- + ---------- + ---------- | 1 + sin(x) /x\ /x\ /x\ | 1 + tan|-| 1 + tan|-| 1 + tan|-| / \2/ \2/ \2/
$$\int \frac{\sin{\left(x \right)}}{\sin{\left(x \right)} + 1}\, dx = C + \frac{x \tan{\left(\frac{x}{2} \right)}}{\tan{\left(\frac{x}{2} \right)} + 1} + \frac{x}{\tan{\left(\frac{x}{2} \right)} + 1} + \frac{2}{\tan{\left(\frac{x}{2} \right)} + 1}$$
Gráfica
Respuesta
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3 tan(1/2)
-2 + ------------ + ------------
1 + tan(1/2) 1 + tan(1/2)
$$-2 + \frac{\tan{\left(\frac{1}{2} \right)}}{\tan{\left(\frac{1}{2} \right)} + 1} + \frac{3}{\tan{\left(\frac{1}{2} \right)} + 1}$$
=
=
3 tan(1/2)
-2 + ------------ + ------------
1 + tan(1/2) 1 + tan(1/2)
$$-2 + \frac{\tan{\left(\frac{1}{2} \right)}}{\tan{\left(\frac{1}{2} \right)} + 1} + \frac{3}{\tan{\left(\frac{1}{2} \right)} + 1}$$
-2 + 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.