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