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