Sr Examen
Integral de lnx/(x^3+1)^(1/3) dx
Solución
Ha introducido
[src]
1 / | | log(x) | ----------- dx | ________ | 3 / 3 | \/ x + 1 | / 0
$$\int\limits_{0}^{1} \frac{\log{\left(x \right)}}{\sqrt[3]{x^{3} + 1}}\, dx$$
Integral(log(x)/(x^3 + 1)^(1/3), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / | | | log(x) | log(x) | ----------- dx = C + | ------------------------- dx | ________ | ______________________ | 3 / 3 | 3 / / 2 \ | \/ x + 1 | \/ (1 + x)*\1 + x - x/ | | / /
$$\int \frac{\log{\left(x \right)}}{\sqrt[3]{x^{3} + 1}}\, dx = C + \int \frac{\log{\left(x \right)}}{\sqrt[3]{\left(x + 1\right) \left(x^{2} - x + 1\right)}}\, dx$$
Respuesta
[src]
1 / | | log(x) | ------------------------- dx | ____________ | 3 _______ 3 / 2 | \/ 1 + x *\/ 1 + x - x | / 0
$$\int\limits_{0}^{1} \frac{\log{\left(x \right)}}{\sqrt[3]{x + 1} \sqrt[3]{x^{2} - x + 1}}\, dx$$
=
=
1 / | | log(x) | ------------------------- dx | ____________ | 3 _______ 3 / 2 | \/ 1 + x *\/ 1 + x - x | / 0
$$\int\limits_{0}^{1} \frac{\log{\left(x \right)}}{\sqrt[3]{x + 1} \sqrt[3]{x^{2} - x + 1}}\, dx$$
Integral(log(x)/((1 + x)^(1/3)*(1 + x^2 - x)^(1/3)), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.