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