Sr Examen
Integral de x*sqrt(1-ln^2*x)/ dx
Solución
Ha introducido
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1/2 e / | | _____________ | / 2 | x*\/ 1 - log (x) dx | / 1
$$\int\limits_{1}^{e^{\frac{1}{2}}} x \sqrt{1 - \log{\left(x \right)}^{2}}\, dx$$
Integral(x*sqrt(1 - log(x)^2), (x, 1, exp(1/2)))
Respuesta (Indefinida)
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/ | / | _____________ | | / 2 | _____________________________ | x*\/ 1 - log (x) dx = C + | x*\/ -(1 + log(x))*(-1 + log(x)) dx | | / /
$$\int x \sqrt{1 - \log{\left(x \right)}^{2}}\, dx = C + \int x \sqrt{- \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)} + 1\right)}\, dx$$
Respuesta
[src]
1/2 e / | | _____________________________ | x*\/ -(1 + log(x))*(-1 + log(x)) dx | / 1
$$\int\limits_{1}^{e^{\frac{1}{2}}} x \sqrt{- \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)} + 1\right)}\, dx$$
=
=
1/2 e / | | _____________________________ | x*\/ -(1 + log(x))*(-1 + log(x)) dx | / 1
$$\int\limits_{1}^{e^{\frac{1}{2}}} x \sqrt{- \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)} + 1\right)}\, dx$$
Integral(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.