Sr Examen
Integral de (3^x)/((3^(2x))+5) dx
Solución
Ha introducido
[src]
1 / | | x | 3 | -------- dx | 2*x | 3 + 5 | / 0
$$\int\limits_{0}^{1} \frac{3^{x}}{3^{2 x} + 5}\, dx$$
Integral(3^x/(3^(2*x) + 5), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / x ___\ | ___ |3 *\/ 5 | | x \/ 5 *atan|--------| | 3 \ 5 / | -------- dx = C + -------------------- | 2*x 5*log(3) | 3 + 5 | /
$$\int \frac{3^{x}}{3^{2 x} + 5}\, dx = C + \frac{\sqrt{5} \operatorname{atan}{\left(\frac{3^{x} \sqrt{5}}{5} \right)}}{5 \log{\left(3 \right)}}$$
Gráfica
Respuesta
[src]
/ 2 \ / 2 \
RootSum\20*z + 1, i -> i*log(81 + 10*i)/ RootSum\20*z + 1, i -> i*log(1 + 10*i)/
----------------------------------------- - ----------------------------------------
log(3) log(3)
$$- \frac{\operatorname{RootSum} {\left(20 z^{2} + 1, \left( i \mapsto i \log{\left(10 i + 1 \right)} \right)\right)}}{\log{\left(3 \right)}} + \frac{\operatorname{RootSum} {\left(20 z^{2} + 1, \left( i \mapsto i \log{\left(10 i + 81 \right)} \right)\right)}}{\log{\left(3 \right)}}$$
=
=
/ 2 \ / 2 \
RootSum\20*z + 1, i -> i*log(81 + 10*i)/ RootSum\20*z + 1, i -> i*log(1 + 10*i)/
----------------------------------------- - ----------------------------------------
log(3) log(3)
$$- \frac{\operatorname{RootSum} {\left(20 z^{2} + 1, \left( i \mapsto i \log{\left(10 i + 1 \right)} \right)\right)}}{\log{\left(3 \right)}} + \frac{\operatorname{RootSum} {\left(20 z^{2} + 1, \left( i \mapsto i \log{\left(10 i + 81 \right)} \right)\right)}}{\log{\left(3 \right)}}$$
RootSum(20*_z^2 + 1, Lambda(_i, _i*log(81 + 10*_i)))/log(3) - RootSum(20*_z^2 + 1, Lambda(_i, _i*log(1 + 10*_i)))/log(3)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.