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