Sr Examen
Integral de 5^x/(4+5^(2*x)) dx
Solución
Ha introducido
[src]
1 / | | x | 5 | -------- dx | 2*x | 4 + 5 | / 0
$$\int\limits_{0}^{1} \frac{5^{x}}{5^{2 x} + 4}\, dx$$
Integral(5^x/(4 + 5^(2*x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / x\ | |5 | | x atan|--| | 5 \2 / | -------- dx = C + -------- | 2*x 2*log(5) | 4 + 5 | /
$$\int \frac{5^{x}}{5^{2 x} + 4}\, dx = C + \frac{\operatorname{atan}{\left(\frac{5^{x}}{2} \right)}}{2 \log{\left(5 \right)}}$$
Gráfica
Respuesta
[src]
/ 2 \ / 2 \
RootSum\16*z + 1, i -> i*log(625 + 8*i)/ RootSum\16*z + 1, i -> i*log(1 + 8*i)/
----------------------------------------- - ---------------------------------------
log(5) log(5)
$$- \frac{\operatorname{RootSum} {\left(16 z^{2} + 1, \left( i \mapsto i \log{\left(8 i + 1 \right)} \right)\right)}}{\log{\left(5 \right)}} + \frac{\operatorname{RootSum} {\left(16 z^{2} + 1, \left( i \mapsto i \log{\left(8 i + 625 \right)} \right)\right)}}{\log{\left(5 \right)}}$$
=
=
/ 2 \ / 2 \
RootSum\16*z + 1, i -> i*log(625 + 8*i)/ RootSum\16*z + 1, i -> i*log(1 + 8*i)/
----------------------------------------- - ---------------------------------------
log(5) log(5)
$$- \frac{\operatorname{RootSum} {\left(16 z^{2} + 1, \left( i \mapsto i \log{\left(8 i + 1 \right)} \right)\right)}}{\log{\left(5 \right)}} + \frac{\operatorname{RootSum} {\left(16 z^{2} + 1, \left( i \mapsto i \log{\left(8 i + 625 \right)} \right)\right)}}{\log{\left(5 \right)}}$$
RootSum(16*_z^2 + 1, Lambda(_i, _i*log(625 + 8*_i)))/log(5) - RootSum(16*_z^2 + 1, Lambda(_i, _i*log(1 + 8*_i)))/log(5)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.