Sr Examen
Integral de 4^x/(1+4^(2x)) dx
Solución
Ha introducido
[src]
1 / | | x | 4 | -------- dx | 2*x | 1 + 4 | / 0
$$\int\limits_{0}^{1} \frac{4^{x}}{4^{2 x} + 1}\, dx$$
Integral(4^x/(1 + 4^(2*x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | | x / x\ | 4 atan\4 / | -------- dx = C + -------- | 2*x 2*log(2) | 1 + 4 | /
$$\int \frac{4^{x}}{4^{2 x} + 1}\, dx = C + \frac{\operatorname{atan}{\left(4^{x} \right)}}{2 \log{\left(2 \right)}}$$
Gráfica
Respuesta
[src]
/ 2 \ / 2 \
RootSum\16*z + 1, i -> i*log(256 + 4*i)/ RootSum\16*z + 1, i -> i*log(1 + 4*i)/
----------------------------------------- - ---------------------------------------
log(2) log(2)
$$- \frac{\operatorname{RootSum} {\left(16 z^{2} + 1, \left( i \mapsto i \log{\left(4 i + 1 \right)} \right)\right)}}{\log{\left(2 \right)}} + \frac{\operatorname{RootSum} {\left(16 z^{2} + 1, \left( i \mapsto i \log{\left(4 i + 256 \right)} \right)\right)}}{\log{\left(2 \right)}}$$
=
=
/ 2 \ / 2 \
RootSum\16*z + 1, i -> i*log(256 + 4*i)/ RootSum\16*z + 1, i -> i*log(1 + 4*i)/
----------------------------------------- - ---------------------------------------
log(2) log(2)
$$- \frac{\operatorname{RootSum} {\left(16 z^{2} + 1, \left( i \mapsto i \log{\left(4 i + 1 \right)} \right)\right)}}{\log{\left(2 \right)}} + \frac{\operatorname{RootSum} {\left(16 z^{2} + 1, \left( i \mapsto i \log{\left(4 i + 256 \right)} \right)\right)}}{\log{\left(2 \right)}}$$
RootSum(16*_z^2 + 1, Lambda(_i, _i*log(256 + 4*_i)))/log(2) - RootSum(16*_z^2 + 1, Lambda(_i, _i*log(1 + 4*_i)))/log(2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.