Sr Examen
Integral de (e^(3/x)-1)/sqrt(x^2+4) dx
Solución
Ha introducido
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oo / | | 3 | - | x | E - 1 | ----------- dx | ________ | / 2 | \/ x + 4 | / 2
$$\int\limits_{2}^{\infty} \frac{e^{\frac{3}{x}} - 1}{\sqrt{x^{2} + 4}}\, dx$$
Integral((E^(3/x) - 1)/sqrt(x^2 + 4), (x, 2, oo))
Respuesta (Indefinida)
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/ / | | | 3 | 3 | - | - | x | x | E - 1 /x\ | e | ----------- dx = C - asinh|-| + | ----------- dx | ________ \2/ | ________ | / 2 | / 2 | \/ x + 4 | \/ 4 + x | | / /
$$\int \frac{e^{\frac{3}{x}} - 1}{\sqrt{x^{2} + 4}}\, dx = C - \operatorname{asinh}{\left(\frac{x}{2} \right)} + \int \frac{e^{\frac{3}{x}}}{\sqrt{x^{2} + 4}}\, dx$$
Respuesta
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oo / | | / 1\ / 1 2\ | | -| | - -| | | x| | x x| | \-1 + e /*\1 + e + e / | ----------------------- dx | ________ | / 2 | \/ 4 + x | / 2
$$\int\limits_{2}^{\infty} \frac{\left(e^{\frac{1}{x}} - 1\right) \left(e^{\frac{2}{x}} + e^{\frac{1}{x}} + 1\right)}{\sqrt{x^{2} + 4}}\, dx$$
=
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oo / | | / 1\ / 1 2\ | | -| | - -| | | x| | x x| | \-1 + e /*\1 + e + e / | ----------------------- dx | ________ | / 2 | \/ 4 + x | / 2
$$\int\limits_{2}^{\infty} \frac{\left(e^{\frac{1}{x}} - 1\right) \left(e^{\frac{2}{x}} + e^{\frac{1}{x}} + 1\right)}{\sqrt{x^{2} + 4}}\, dx$$
Integral((-1 + exp(1/x))*(1 + exp(1/x) + exp(2/x))/sqrt(4 + x^2), (x, 2, oo))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.