Sr Examen
Integral de (xarctgx)/(1+x^5)^(1/3) dx
Solución
Ha introducido
[src]
oo / | | x*atan(x) | ----------- dx | ________ | 3 / 5 | \/ 1 + x | / 1
$$\int\limits_{1}^{\infty} \frac{x \operatorname{atan}{\left(x \right)}}{\sqrt[3]{x^{5} + 1}}\, dx$$
Integral((x*atan(x))/(1 + x^5)^(1/3), (x, 1, oo))
Respuesta (Indefinida)
[src]
/ / | | | x*atan(x) | x*atan(x) | ----------- dx = C + | ----------------------------------- dx | ________ | ________________________________ | 3 / 5 | 3 / / 2 4 3\ | \/ 1 + x | \/ (1 + x)*\1 + x + x - x - x / | | / /
$$\int \frac{x \operatorname{atan}{\left(x \right)}}{\sqrt[3]{x^{5} + 1}}\, dx = C + \int \frac{x \operatorname{atan}{\left(x \right)}}{\sqrt[3]{\left(x + 1\right) \left(x^{4} - x^{3} + x^{2} - x + 1\right)}}\, dx$$
Respuesta
[src]
oo / | | x*atan(x) | ----------------------------------- dx | ________________________________ | 3 / / 2 4 3\ | \/ (1 + x)*\1 + x + x - x - x / | / 1
$$\int\limits_{1}^{\infty} \frac{x \operatorname{atan}{\left(x \right)}}{\sqrt[3]{\left(x + 1\right) \left(x^{4} - x^{3} + x^{2} - x + 1\right)}}\, dx$$
=
=
oo / | | x*atan(x) | ----------------------------------- dx | ________________________________ | 3 / / 2 4 3\ | \/ (1 + x)*\1 + x + x - x - x / | / 1
$$\int\limits_{1}^{\infty} \frac{x \operatorname{atan}{\left(x \right)}}{\sqrt[3]{\left(x + 1\right) \left(x^{4} - x^{3} + x^{2} - x + 1\right)}}\, dx$$
Integral(x*atan(x)/((1 + x)*(1 + x^2 + x^4 - x - x^3))^(1/3), (x, 1, oo))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.