Sr Examen
Integral de ln3x/(1+((ln^2)3x))x dx
Solución
Ha introducido
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1 / | | log(3*x) | ---------------*x dx | 2 | 1 + log (x)*3*x | / 0
$$\int\limits_{0}^{1} x \frac{\log{\left(3 x \right)}}{x 3 \log{\left(x \right)}^{2} + 1}\, dx$$
Integral((log(3*x)/(1 + (log(x)^2*3)*x))*x, (x, 0, 1))
Respuesta (Indefinida)
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/ / / \ / | | | | | | log(3*x) | | x | | x*log(x) | ---------------*x dx = C + | | --------------- dx|*log(3) + | --------------- dx | 2 | | 2 | | 2 | 1 + log (x)*3*x | | 1 + 3*x*log (x) | | 1 + 3*x*log (x) | | | | | / \/ / /
$$\int x \frac{\log{\left(3 x \right)}}{x 3 \log{\left(x \right)}^{2} + 1}\, dx = C + \log{\left(3 \right)} \int \frac{x}{3 x \log{\left(x \right)}^{2} + 1}\, dx + \int \frac{x \log{\left(x \right)}}{3 x \log{\left(x \right)}^{2} + 1}\, dx$$
Respuesta
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1 / | | x*(log(3) + log(x)) | ------------------- dx | 2 | 1 + 3*x*log (x) | / 0
$$\int\limits_{0}^{1} \frac{x \left(\log{\left(x \right)} + \log{\left(3 \right)}\right)}{3 x \log{\left(x \right)}^{2} + 1}\, dx$$
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1 / | | x*(log(3) + log(x)) | ------------------- dx | 2 | 1 + 3*x*log (x) | / 0
$$\int\limits_{0}^{1} \frac{x \left(\log{\left(x \right)} + \log{\left(3 \right)}\right)}{3 x \log{\left(x \right)}^{2} + 1}\, dx$$
Integral(x*(log(3) + log(x))/(1 + 3*x*log(x)^2), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.