Sr Examen
Integral de (lnx)/(xscrt(1–((lnx)^4))) dx
Solución
Ha introducido
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1/2 e / | | log(x) | ------------------ dx | _____________ | / 4 | x*\/ 1 - log (x) | / 1
$$\int\limits_{1}^{e^{\frac{1}{2}}} \frac{\log{\left(x \right)}}{x \sqrt{1 - \log{\left(x \right)}^{4}}}\, dx$$
Integral(log(x)/((x*sqrt(1 - log(x)^4))), (x, 1, exp(1/2)))
Respuesta (Indefinida)
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/ / | | | 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]
1/2 e / | | log(x) | -------------------------------------------------- dx | _____________ | _____________________________ / 2 | x*\/ -(1 + log(x))*(-1 + log(x)) *\/ 1 + log (x) | / 1
$$\int\limits_{1}^{e^{\frac{1}{2}}} \frac{\log{\left(x \right)}}{x \sqrt{- \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)} + 1\right)} \sqrt{\log{\left(x \right)}^{2} + 1}}\, dx$$
=
=
1/2 e / | | log(x) | -------------------------------------------------- dx | _____________ | _____________________________ / 2 | x*\/ -(1 + log(x))*(-1 + log(x)) *\/ 1 + log (x) | / 1
$$\int\limits_{1}^{e^{\frac{1}{2}}} \frac{\log{\left(x \right)}}{x \sqrt{- \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)} + 1\right)} \sqrt{\log{\left(x \right)}^{2} + 1}}\, dx$$
Integral(log(x)/(x*sqrt(-(1 + log(x))*(-1 + log(x)))*sqrt(1 + log(x)^2)), (x, 1, exp(1/2)))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.