Sr Examen
Integral de 3*dx/(e^(2*x)-2*e^x+3) dx
Solución
Ha introducido
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1 / | | 3 | --------------- dx | 2*x x | E - 2*E + 3 | / 0
$$\int\limits_{0}^{1} \frac{3}{\left(- 2 e^{x} + e^{2 x}\right) + 3}\, dx$$
Integral(3/(E^(2*x) - 2*exp(x) + 3), (x, 0, 1))
Respuesta (Indefinida)
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/ ___ / x\\ / ___ |\/ 2 *\-1 + E /| | / x 2*x\ \/ 2 *atan|---------------| | 3 log\3 - 2*e + e / \ 2 / / x\ | --------------- dx = C - -------------------- + --------------------------- + log\E / | 2*x x 2 2 | E - 2*E + 3 | /
$$\int \frac{3}{\left(- 2 e^{x} + e^{2 x}\right) + 3}\, dx = C + \log{\left(e^{x} \right)} - \frac{\log{\left(e^{2 x} - 2 e^{x} + 3 \right)}}{2} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} \left(e^{x} - 1\right)}{2} \right)}}{2}$$
Gráfica
Respuesta
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/ 2 \ / 2 \ 1 - RootSum\8*z + 8*z + 3, i -> i*log(2 + 4*i)/ + RootSum\8*z + 8*z + 3, i -> i*log(1 + E + 4*i)/
$$- \operatorname{RootSum} {\left(8 z^{2} + 8 z + 3, \left( i \mapsto i \log{\left(4 i + 2 \right)} \right)\right)} + \operatorname{RootSum} {\left(8 z^{2} + 8 z + 3, \left( i \mapsto i \log{\left(4 i + 1 + e \right)} \right)\right)} + 1$$
=
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/ 2 \ / 2 \ 1 - RootSum\8*z + 8*z + 3, i -> i*log(2 + 4*i)/ + RootSum\8*z + 8*z + 3, i -> i*log(1 + E + 4*i)/
$$- \operatorname{RootSum} {\left(8 z^{2} + 8 z + 3, \left( i \mapsto i \log{\left(4 i + 2 \right)} \right)\right)} + \operatorname{RootSum} {\left(8 z^{2} + 8 z + 3, \left( i \mapsto i \log{\left(4 i + 1 + e \right)} \right)\right)} + 1$$
1 - RootSum(8*_z^2 + 8*_z + 3, Lambda(_i, _i*log(2 + 4*_i))) + RootSum(8*_z^2 + 8*_z + 3, Lambda(_i, _i*log(1 + E + 4*_i)))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.