Sr Examen
Integral de ((2^x)+(3^x))/(6^(x+1)) dx
Solución
Ha introducido
[src]
1 / | | x x | 2 + 3 | ------- dx | x + 1 | 6 | / 0
$$\int\limits_{0}^{1} \frac{2^{x} + 3^{x}}{6^{x + 1}}\, dx$$
Integral((2^x + 3^x)/6^(x + 1), (x, 0, 1))
Gráfica
Respuesta
[src]
log(2) log(3) 5*log(6) 2*log(6) 2*log(3) 3*log(2)
- --------------------------------------------------------------- - --------------------------------------------------------------- - ------------------------------------------------------------------- + --------------------------------------------------------------- + ------------------------------------------------------------------- + -------------------------------------------------------------------
2 2 2 2 2 2
6*log (6) - 6*log(2)*log(6) - 6*log(3)*log(6) + 6*log(2)*log(3) 6*log (6) - 6*log(2)*log(6) - 6*log(3)*log(6) + 6*log(2)*log(3) 36*log (6) - 36*log(2)*log(6) - 36*log(3)*log(6) + 36*log(2)*log(3) 6*log (6) - 6*log(2)*log(6) - 6*log(3)*log(6) + 6*log(2)*log(3) 36*log (6) - 36*log(2)*log(6) - 36*log(3)*log(6) + 36*log(2)*log(3) 36*log (6) - 36*log(2)*log(6) - 36*log(3)*log(6) + 36*log(2)*log(3)
$$- \frac{5 \log{\left(6 \right)}}{- 36 \log{\left(3 \right)} \log{\left(6 \right)} - 36 \log{\left(2 \right)} \log{\left(6 \right)} + 36 \log{\left(2 \right)} \log{\left(3 \right)} + 36 \log{\left(6 \right)}^{2}} - \frac{\log{\left(3 \right)}}{- 6 \log{\left(3 \right)} \log{\left(6 \right)} - 6 \log{\left(2 \right)} \log{\left(6 \right)} + 6 \log{\left(2 \right)} \log{\left(3 \right)} + 6 \log{\left(6 \right)}^{2}} - \frac{\log{\left(2 \right)}}{- 6 \log{\left(3 \right)} \log{\left(6 \right)} - 6 \log{\left(2 \right)} \log{\left(6 \right)} + 6 \log{\left(2 \right)} \log{\left(3 \right)} + 6 \log{\left(6 \right)}^{2}} + \frac{3 \log{\left(2 \right)}}{- 36 \log{\left(3 \right)} \log{\left(6 \right)} - 36 \log{\left(2 \right)} \log{\left(6 \right)} + 36 \log{\left(2 \right)} \log{\left(3 \right)} + 36 \log{\left(6 \right)}^{2}} + \frac{2 \log{\left(3 \right)}}{- 36 \log{\left(3 \right)} \log{\left(6 \right)} - 36 \log{\left(2 \right)} \log{\left(6 \right)} + 36 \log{\left(2 \right)} \log{\left(3 \right)} + 36 \log{\left(6 \right)}^{2}} + \frac{2 \log{\left(6 \right)}}{- 6 \log{\left(3 \right)} \log{\left(6 \right)} - 6 \log{\left(2 \right)} \log{\left(6 \right)} + 6 \log{\left(2 \right)} \log{\left(3 \right)} + 6 \log{\left(6 \right)}^{2}}$$
=
=
log(2) log(3) 5*log(6) 2*log(6) 2*log(3) 3*log(2)
- --------------------------------------------------------------- - --------------------------------------------------------------- - ------------------------------------------------------------------- + --------------------------------------------------------------- + ------------------------------------------------------------------- + -------------------------------------------------------------------
2 2 2 2 2 2
6*log (6) - 6*log(2)*log(6) - 6*log(3)*log(6) + 6*log(2)*log(3) 6*log (6) - 6*log(2)*log(6) - 6*log(3)*log(6) + 6*log(2)*log(3) 36*log (6) - 36*log(2)*log(6) - 36*log(3)*log(6) + 36*log(2)*log(3) 6*log (6) - 6*log(2)*log(6) - 6*log(3)*log(6) + 6*log(2)*log(3) 36*log (6) - 36*log(2)*log(6) - 36*log(3)*log(6) + 36*log(2)*log(3) 36*log (6) - 36*log(2)*log(6) - 36*log(3)*log(6) + 36*log(2)*log(3)
$$- \frac{5 \log{\left(6 \right)}}{- 36 \log{\left(3 \right)} \log{\left(6 \right)} - 36 \log{\left(2 \right)} \log{\left(6 \right)} + 36 \log{\left(2 \right)} \log{\left(3 \right)} + 36 \log{\left(6 \right)}^{2}} - \frac{\log{\left(3 \right)}}{- 6 \log{\left(3 \right)} \log{\left(6 \right)} - 6 \log{\left(2 \right)} \log{\left(6 \right)} + 6 \log{\left(2 \right)} \log{\left(3 \right)} + 6 \log{\left(6 \right)}^{2}} - \frac{\log{\left(2 \right)}}{- 6 \log{\left(3 \right)} \log{\left(6 \right)} - 6 \log{\left(2 \right)} \log{\left(6 \right)} + 6 \log{\left(2 \right)} \log{\left(3 \right)} + 6 \log{\left(6 \right)}^{2}} + \frac{3 \log{\left(2 \right)}}{- 36 \log{\left(3 \right)} \log{\left(6 \right)} - 36 \log{\left(2 \right)} \log{\left(6 \right)} + 36 \log{\left(2 \right)} \log{\left(3 \right)} + 36 \log{\left(6 \right)}^{2}} + \frac{2 \log{\left(3 \right)}}{- 36 \log{\left(3 \right)} \log{\left(6 \right)} - 36 \log{\left(2 \right)} \log{\left(6 \right)} + 36 \log{\left(2 \right)} \log{\left(3 \right)} + 36 \log{\left(6 \right)}^{2}} + \frac{2 \log{\left(6 \right)}}{- 6 \log{\left(3 \right)} \log{\left(6 \right)} - 6 \log{\left(2 \right)} \log{\left(6 \right)} + 6 \log{\left(2 \right)} \log{\left(3 \right)} + 6 \log{\left(6 \right)}^{2}}$$
-log(2)/(6*log(6)^2 - 6*log(2)*log(6) - 6*log(3)*log(6) + 6*log(2)*log(3)) - log(3)/(6*log(6)^2 - 6*log(2)*log(6) - 6*log(3)*log(6) + 6*log(2)*log(3)) - 5*log(6)/(36*log(6)^2 - 36*log(2)*log(6) - 36*log(3)*log(6) + 36*log(2)*log(3)) + 2*log(6)/(6*log(6)^2 - 6*log(2)*log(6) - 6*log(3)*log(6) + 6*log(2)*log(3)) + 2*log(3)/(36*log(6)^2 - 36*log(2)*log(6) - 36*log(3)*log(6) + 36*log(2)*log(3)) + 3*log(2)/(36*log(6)^2 - 36*log(2)*log(6) - 36*log(3)*log(6) + 36*log(2)*log(3))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.