Sr Examen
Integral de 3^x/(1+3^(2*x)) dx
Solución
Ha introducido
[src]
1/2 / | | x | 3 | -------- dx | 2*x | 1 + 3 | / -1/2
$$\int\limits_{- \frac{1}{2}}^{\frac{1}{2}} \frac{3^{x}}{3^{2 x} + 1}\, dx$$
Integral(3^x/(1 + 3^(2*x)), (x, -1/2, 1/2))
Respuesta (Indefinida)
[src]
/ | | x / x\ | 3 atan\3 / | -------- dx = C + -------- | 2*x log(3) | 1 + 3 | /
$$\int \frac{3^{x}}{3^{2 x} + 1}\, dx = C + \frac{\operatorname{atan}{\left(3^{x} \right)}}{\log{\left(3 \right)}}$$
Gráfica
Respuesta
[src]
/ 2 \ / 2 \
RootSum\4*z + 1, i -> i*log(9 + 2*i)/ RootSum\4*z + 1, i -> i*log(1/9 + 2*i)/
-------------------------------------- - ----------------------------------------
log(3) log(3)
$$- \frac{\operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + \frac{1}{9} \right)} \right)\right)}}{\log{\left(3 \right)}} + \frac{\operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + 9 \right)} \right)\right)}}{\log{\left(3 \right)}}$$
=
=
/ 2 \ / 2 \
RootSum\4*z + 1, i -> i*log(9 + 2*i)/ RootSum\4*z + 1, i -> i*log(1/9 + 2*i)/
-------------------------------------- - ----------------------------------------
log(3) log(3)
$$- \frac{\operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + \frac{1}{9} \right)} \right)\right)}}{\log{\left(3 \right)}} + \frac{\operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + 9 \right)} \right)\right)}}{\log{\left(3 \right)}}$$
RootSum(4*_z^2 + 1, Lambda(_i, _i*log(9 + 2*_i)))/log(3) - RootSum(4*_z^2 + 1, Lambda(_i, _i*log(1/9 + 2*_i)))/log(3)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.