Sr Examen
Integral de arcctg(5x)/((1-25x^2)(1+25x^2)) dx
Solución
Ha introducido
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1 / | | acot(5*x) | ----------------------- dx | / 2\ / 2\ | \1 - 25*x /*\1 + 25*x / | / 0
$$\int\limits_{0}^{1} \frac{\operatorname{acot}{\left(5 x \right)}}{\left(1 - 25 x^{2}\right) \left(25 x^{2} + 1\right)}\, dx$$
Integral(acot(5*x)/(((1 - 25*x^2)*(1 + 25*x^2))), (x, 0, 1))
Respuesta (Indefinida)
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/ / | | | acot(5*x) | acot(5*x) | ----------------------- dx = C - | -------------------------------- dx | / 2\ / 2\ | / 2\ | \1 - 25*x /*\1 + 25*x / | (1 + 5*x)*\1 + 25*x /*(-1 + 5*x) | | / /
$$\int \frac{\operatorname{acot}{\left(5 x \right)}}{\left(1 - 25 x^{2}\right) \left(25 x^{2} + 1\right)}\, dx = C - \int \frac{\operatorname{acot}{\left(5 x \right)}}{\left(5 x - 1\right) \left(5 x + 1\right) \left(25 x^{2} + 1\right)}\, dx$$
Respuesta
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1 / | | acot(5*x) - | ----------- dx | 4 | -1 + 625*x | / 0
$$- \int\limits_{0}^{1} \frac{\operatorname{acot}{\left(5 x \right)}}{625 x^{4} - 1}\, dx$$
=
=
1 / | | acot(5*x) - | ----------- dx | 4 | -1 + 625*x | / 0
$$- \int\limits_{0}^{1} \frac{\operatorname{acot}{\left(5 x \right)}}{625 x^{4} - 1}\, dx$$
-Integral(acot(5*x)/(-1 + 625*x^4), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.