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