Sr Examen
Integral de lnx/(x*sqrt(1-(ln(x)^4))) dx
Solución
Ha introducido
[src]
0 / | | log(x) | ------------------ dx | _____________ | / 4 | x*\/ 1 - log (x) | / 4
$$\int\limits_{4}^{0} \frac{\log{\left(x \right)}}{x \sqrt{1 - \log{\left(x \right)}^{4}}}\, dx$$
Integral(log(x)/((x*sqrt(1 - log(x)^4))), (x, 4, 0))
Respuesta (Indefinida)
[src]
/ / | | | log(x) | log(x) | ------------------ dx = C + | ------------------------------------------------ dx | _____________ | ___________________________________________ | / 4 | / / 2 \ | x*\/ 1 - log (x) | x*\/ -\1 + log (x)/*(1 + log(x))*(-1 + log(x)) | | / /
$$\int \frac{\log{\left(x \right)}}{x \sqrt{1 - \log{\left(x \right)}^{4}}}\, dx = C + \int \frac{\log{\left(x \right)}}{x \sqrt{- \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)} + 1\right) \left(\log{\left(x \right)}^{2} + 1\right)}}\, dx$$
Respuesta
[src]
0 / | | log(x) | -------------------------------------------------- dx | _____________ | _____________________________ / 2 | x*\/ -(1 + log(x))*(-1 + log(x)) *\/ 1 + log (x) | / 4
$$\int\limits_{4}^{0} \frac{\log{\left(x \right)}}{x \sqrt{- \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)} + 1\right)} \sqrt{\log{\left(x \right)}^{2} + 1}}\, dx$$
=
=
0 / | | log(x) | -------------------------------------------------- dx | _____________ | _____________________________ / 2 | x*\/ -(1 + log(x))*(-1 + log(x)) *\/ 1 + log (x) | / 4
$$\int\limits_{4}^{0} \frac{\log{\left(x \right)}}{x \sqrt{- \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)} + 1\right)} \sqrt{\log{\left(x \right)}^{2} + 1}}\, dx$$
Integral(log(x)/(x*sqrt(-(1 + log(x))*(-1 + log(x)))*sqrt(1 + log(x)^2)), (x, 4, 0))
Respuesta numérica
[src]
(-0.0323884442358661 - 3.41887875976503j)
(-0.0323884442358661 - 3.41887875976503j)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.