Sr Examen
Integral de 2*e^x/(3+e)^x dx
Solución
Ha introducido
[src]
1 / | | x | 2*E | -------- dx | x | (3 + E) | / 0
$$\int\limits_{0}^{1} \frac{2 e^{x}}{\left(e + 3\right)^{x}}\, dx$$
Integral((2*E^x)/(3 + E)^x, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | | x x | 2*E 2*e | -------- dx = C - -------------------------------- | x x x | (3 + E) - (3 + E) + (3 + E) *log(3 + E) | /
$$\int \frac{2 e^{x}}{\left(e + 3\right)^{x}}\, dx = C - \frac{2 e^{x}}{- \left(e + 3\right)^{x} + \left(e + 3\right)^{x} \log{\left(e + 3 \right)}}$$
Gráfica
Respuesta
[src]
1
-1 + ----------
log(3 + E)
2 2*(3 + E)
--------------------------- - ---------------------------
/ 1 \ / 1 \
|1 - ----------|*log(3 + E) |1 - ----------|*log(3 + E)
\ log(3 + E)/ \ log(3 + E)/
$$- \frac{2}{\left(1 - \frac{1}{\log{\left(e + 3 \right)}}\right) \left(e + 3\right)^{1 - \frac{1}{\log{\left(e + 3 \right)}}} \log{\left(e + 3 \right)}} + \frac{2}{\left(1 - \frac{1}{\log{\left(e + 3 \right)}}\right) \log{\left(e + 3 \right)}}$$
=
=
1
-1 + ----------
log(3 + E)
2 2*(3 + E)
--------------------------- - ---------------------------
/ 1 \ / 1 \
|1 - ----------|*log(3 + E) |1 - ----------|*log(3 + E)
\ log(3 + E)/ \ log(3 + E)/
$$- \frac{2}{\left(1 - \frac{1}{\log{\left(e + 3 \right)}}\right) \left(e + 3\right)^{1 - \frac{1}{\log{\left(e + 3 \right)}}} \log{\left(e + 3 \right)}} + \frac{2}{\left(1 - \frac{1}{\log{\left(e + 3 \right)}}\right) \log{\left(e + 3 \right)}}$$
2/((1 - 1/log(3 + E))*log(3 + E)) - 2*(3 + E)^(-1 + 1/log(3 + E))/((1 - 1/log(3 + E))*log(3 + E))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.