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