Sr Examen
Integral de (2^(x+1)-5^(x+1))/10^(x+2) dx
Solución
Ha introducido
[src]
1 / | | x + 1 x + 1 | 2 - 5 | --------------- dx | x + 2 | 10 | / 0
$$\int\limits_{0}^{1} \frac{2^{x + 1} - 5^{x + 1}}{10^{x + 2}}\, dx$$
Integral((2^(x + 1) - 5^(x + 1))/10^(x + 2), (x, 0, 1))
Gráfica
Respuesta
[src]
25*log(2) 3*log(10) 2*log(5) 4*log(5) 5*log(2) 21*log(10)
- ------------------------------------------------------------------------------ - -------------------------------------------------------------------------- - -------------------------------------------------------------------------- + ------------------------------------------------------------------------------ + -------------------------------------------------------------------------- + ------------------------------------------------------------------------------
2 2 2 2 2 2
1000*log (10) - 1000*log(2)*log(10) - 1000*log(5)*log(10) + 1000*log(2)*log(5) 100*log (10) - 100*log(2)*log(10) - 100*log(5)*log(10) + 100*log(2)*log(5) 100*log (10) - 100*log(2)*log(10) - 100*log(5)*log(10) + 100*log(2)*log(5) 1000*log (10) - 1000*log(2)*log(10) - 1000*log(5)*log(10) + 1000*log(2)*log(5) 100*log (10) - 100*log(2)*log(10) - 100*log(5)*log(10) + 100*log(2)*log(5) 1000*log (10) - 1000*log(2)*log(10) - 1000*log(5)*log(10) + 1000*log(2)*log(5)
$$- \frac{3 \log{\left(10 \right)}}{- 100 \log{\left(5 \right)} \log{\left(10 \right)} - 100 \log{\left(2 \right)} \log{\left(10 \right)} + 100 \log{\left(2 \right)} \log{\left(5 \right)} + 100 \log{\left(10 \right)}^{2}} - \frac{2 \log{\left(5 \right)}}{- 100 \log{\left(5 \right)} \log{\left(10 \right)} - 100 \log{\left(2 \right)} \log{\left(10 \right)} + 100 \log{\left(2 \right)} \log{\left(5 \right)} + 100 \log{\left(10 \right)}^{2}} - \frac{25 \log{\left(2 \right)}}{- 1000 \log{\left(5 \right)} \log{\left(10 \right)} - 1000 \log{\left(2 \right)} \log{\left(10 \right)} + 1000 \log{\left(2 \right)} \log{\left(5 \right)} + 1000 \log{\left(10 \right)}^{2}} + \frac{4 \log{\left(5 \right)}}{- 1000 \log{\left(5 \right)} \log{\left(10 \right)} - 1000 \log{\left(2 \right)} \log{\left(10 \right)} + 1000 \log{\left(2 \right)} \log{\left(5 \right)} + 1000 \log{\left(10 \right)}^{2}} + \frac{5 \log{\left(2 \right)}}{- 100 \log{\left(5 \right)} \log{\left(10 \right)} - 100 \log{\left(2 \right)} \log{\left(10 \right)} + 100 \log{\left(2 \right)} \log{\left(5 \right)} + 100 \log{\left(10 \right)}^{2}} + \frac{21 \log{\left(10 \right)}}{- 1000 \log{\left(5 \right)} \log{\left(10 \right)} - 1000 \log{\left(2 \right)} \log{\left(10 \right)} + 1000 \log{\left(2 \right)} \log{\left(5 \right)} + 1000 \log{\left(10 \right)}^{2}}$$
=
=
25*log(2) 3*log(10) 2*log(5) 4*log(5) 5*log(2) 21*log(10)
- ------------------------------------------------------------------------------ - -------------------------------------------------------------------------- - -------------------------------------------------------------------------- + ------------------------------------------------------------------------------ + -------------------------------------------------------------------------- + ------------------------------------------------------------------------------
2 2 2 2 2 2
1000*log (10) - 1000*log(2)*log(10) - 1000*log(5)*log(10) + 1000*log(2)*log(5) 100*log (10) - 100*log(2)*log(10) - 100*log(5)*log(10) + 100*log(2)*log(5) 100*log (10) - 100*log(2)*log(10) - 100*log(5)*log(10) + 100*log(2)*log(5) 1000*log (10) - 1000*log(2)*log(10) - 1000*log(5)*log(10) + 1000*log(2)*log(5) 100*log (10) - 100*log(2)*log(10) - 100*log(5)*log(10) + 100*log(2)*log(5) 1000*log (10) - 1000*log(2)*log(10) - 1000*log(5)*log(10) + 1000*log(2)*log(5)
$$- \frac{3 \log{\left(10 \right)}}{- 100 \log{\left(5 \right)} \log{\left(10 \right)} - 100 \log{\left(2 \right)} \log{\left(10 \right)} + 100 \log{\left(2 \right)} \log{\left(5 \right)} + 100 \log{\left(10 \right)}^{2}} - \frac{2 \log{\left(5 \right)}}{- 100 \log{\left(5 \right)} \log{\left(10 \right)} - 100 \log{\left(2 \right)} \log{\left(10 \right)} + 100 \log{\left(2 \right)} \log{\left(5 \right)} + 100 \log{\left(10 \right)}^{2}} - \frac{25 \log{\left(2 \right)}}{- 1000 \log{\left(5 \right)} \log{\left(10 \right)} - 1000 \log{\left(2 \right)} \log{\left(10 \right)} + 1000 \log{\left(2 \right)} \log{\left(5 \right)} + 1000 \log{\left(10 \right)}^{2}} + \frac{4 \log{\left(5 \right)}}{- 1000 \log{\left(5 \right)} \log{\left(10 \right)} - 1000 \log{\left(2 \right)} \log{\left(10 \right)} + 1000 \log{\left(2 \right)} \log{\left(5 \right)} + 1000 \log{\left(10 \right)}^{2}} + \frac{5 \log{\left(2 \right)}}{- 100 \log{\left(5 \right)} \log{\left(10 \right)} - 100 \log{\left(2 \right)} \log{\left(10 \right)} + 100 \log{\left(2 \right)} \log{\left(5 \right)} + 100 \log{\left(10 \right)}^{2}} + \frac{21 \log{\left(10 \right)}}{- 1000 \log{\left(5 \right)} \log{\left(10 \right)} - 1000 \log{\left(2 \right)} \log{\left(10 \right)} + 1000 \log{\left(2 \right)} \log{\left(5 \right)} + 1000 \log{\left(10 \right)}^{2}}$$
-25*log(2)/(1000*log(10)^2 - 1000*log(2)*log(10) - 1000*log(5)*log(10) + 1000*log(2)*log(5)) - 3*log(10)/(100*log(10)^2 - 100*log(2)*log(10) - 100*log(5)*log(10) + 100*log(2)*log(5)) - 2*log(5)/(100*log(10)^2 - 100*log(2)*log(10) - 100*log(5)*log(10) + 100*log(2)*log(5)) + 4*log(5)/(1000*log(10)^2 - 1000*log(2)*log(10) - 1000*log(5)*log(10) + 1000*log(2)*log(5)) + 5*log(2)/(100*log(10)^2 - 100*log(2)*log(10) - 100*log(5)*log(10) + 100*log(2)*log(5)) + 21*log(10)/(1000*log(10)^2 - 1000*log(2)*log(10) - 1000*log(5)*log(10) + 1000*log(2)*log(5))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.