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