Sr Examen
Integral de x*ln(x)dx/(x*(1+x^5+x^10)^(1/2)) dx
Solución
Ha introducido
[src]
oo / | | x*log(x) | ------------------- dx | ______________ | / 5 10 | x*\/ 1 + x + x | / 1
$$\int\limits_{1}^{\infty} \frac{x \log{\left(x \right)}}{x \sqrt{x^{10} + \left(x^{5} + 1\right)}}\, dx$$
Integral((x*log(x))/((x*sqrt(1 + x^5 + x^10))), (x, 1, oo))
Respuesta (Indefinida)
[src]
/ / | | | x*log(x) | log(x) | ------------------- dx = C + | -------------------------------------------------- dx | ______________ | _______________________________________________ | / 5 10 | / / 2\ / 3 5 8 4 7\ | x*\/ 1 + x + x | \/ \1 + x + x /*\1 + x + x + x - x - x - x / | | / /
$$\int \frac{x \log{\left(x \right)}}{x \sqrt{x^{10} + \left(x^{5} + 1\right)}}\, dx = C + \int \frac{\log{\left(x \right)}}{\sqrt{\left(x^{2} + x + 1\right) \left(x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1\right)}}\, dx$$
Respuesta
[src]
oo / | | log(x) | -------------------------------------------------- dx | _______________________________________________ | / / 2\ / 3 5 8 4 7\ | \/ \1 + x + x /*\1 + x + x + x - x - x - x / | / 1
$$\int\limits_{1}^{\infty} \frac{\log{\left(x \right)}}{\sqrt{\left(x^{2} + x + 1\right) \left(x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1\right)}}\, dx$$
=
=
oo / | | log(x) | -------------------------------------------------- dx | _______________________________________________ | / / 2\ / 3 5 8 4 7\ | \/ \1 + x + x /*\1 + x + x + x - x - x - x / | / 1
$$\int\limits_{1}^{\infty} \frac{\log{\left(x \right)}}{\sqrt{\left(x^{2} + x + 1\right) \left(x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1\right)}}\, dx$$
Integral(log(x)/sqrt((1 + x + x^2)*(1 + x^3 + x^5 + x^8 - x - x^4 - x^7)), (x, 1, oo))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.