Sr Examen
Integral de (10^x+3*5^(x+2))/(2^x) dx
Solución
Ha introducido
[src]
1 / | | x x + 2 | 10 + 3*5 | -------------- dx | x | 2 | / 0
$$\int\limits_{0}^{1} \frac{10^{x} + 3 \cdot 5^{x + 2}}{2^{x}}\, dx$$
Integral((10^x + 3*5^(x + 2))/2^x, (x, 0, 1))
Gráfica
Respuesta
[src]
log(5) 375*log(10) 76*log(2) 10*log(5) 75*log(10) 385*log(2)
----------------------------------------------------------- - ------------------------------------------------------------------- - ----------------------------------------------------------- - ------------------------------------------------------------------- + ----------------------------------------------------------- + -------------------------------------------------------------------
2 2 2 2 2 2
- log (2) + log(2)*log(5) + log(2)*log(10) - log(5)*log(10) - 2*log (2) - 2*log(5)*log(10) + 2*log(2)*log(5) + 2*log(2)*log(10) - log (2) + log(2)*log(5) + log(2)*log(10) - log(5)*log(10) - 2*log (2) - 2*log(5)*log(10) + 2*log(2)*log(5) + 2*log(2)*log(10) - log (2) + log(2)*log(5) + log(2)*log(10) - log(5)*log(10) - 2*log (2) - 2*log(5)*log(10) + 2*log(2)*log(5) + 2*log(2)*log(10)
$$\frac{75 \log{\left(10 \right)}}{- \log{\left(5 \right)} \log{\left(10 \right)} - \log{\left(2 \right)}^{2} + \log{\left(2 \right)} \log{\left(5 \right)} + \log{\left(2 \right)} \log{\left(10 \right)}} + \frac{385 \log{\left(2 \right)}}{- 2 \log{\left(5 \right)} \log{\left(10 \right)} - 2 \log{\left(2 \right)}^{2} + 2 \log{\left(2 \right)} \log{\left(5 \right)} + 2 \log{\left(2 \right)} \log{\left(10 \right)}} + \frac{\log{\left(5 \right)}}{- \log{\left(5 \right)} \log{\left(10 \right)} - \log{\left(2 \right)}^{2} + \log{\left(2 \right)} \log{\left(5 \right)} + \log{\left(2 \right)} \log{\left(10 \right)}} - \frac{10 \log{\left(5 \right)}}{- 2 \log{\left(5 \right)} \log{\left(10 \right)} - 2 \log{\left(2 \right)}^{2} + 2 \log{\left(2 \right)} \log{\left(5 \right)} + 2 \log{\left(2 \right)} \log{\left(10 \right)}} - \frac{76 \log{\left(2 \right)}}{- \log{\left(5 \right)} \log{\left(10 \right)} - \log{\left(2 \right)}^{2} + \log{\left(2 \right)} \log{\left(5 \right)} + \log{\left(2 \right)} \log{\left(10 \right)}} - \frac{375 \log{\left(10 \right)}}{- 2 \log{\left(5 \right)} \log{\left(10 \right)} - 2 \log{\left(2 \right)}^{2} + 2 \log{\left(2 \right)} \log{\left(5 \right)} + 2 \log{\left(2 \right)} \log{\left(10 \right)}}$$
=
=
log(5) 375*log(10) 76*log(2) 10*log(5) 75*log(10) 385*log(2)
----------------------------------------------------------- - ------------------------------------------------------------------- - ----------------------------------------------------------- - ------------------------------------------------------------------- + ----------------------------------------------------------- + -------------------------------------------------------------------
2 2 2 2 2 2
- log (2) + log(2)*log(5) + log(2)*log(10) - log(5)*log(10) - 2*log (2) - 2*log(5)*log(10) + 2*log(2)*log(5) + 2*log(2)*log(10) - log (2) + log(2)*log(5) + log(2)*log(10) - log(5)*log(10) - 2*log (2) - 2*log(5)*log(10) + 2*log(2)*log(5) + 2*log(2)*log(10) - log (2) + log(2)*log(5) + log(2)*log(10) - log(5)*log(10) - 2*log (2) - 2*log(5)*log(10) + 2*log(2)*log(5) + 2*log(2)*log(10)
$$\frac{75 \log{\left(10 \right)}}{- \log{\left(5 \right)} \log{\left(10 \right)} - \log{\left(2 \right)}^{2} + \log{\left(2 \right)} \log{\left(5 \right)} + \log{\left(2 \right)} \log{\left(10 \right)}} + \frac{385 \log{\left(2 \right)}}{- 2 \log{\left(5 \right)} \log{\left(10 \right)} - 2 \log{\left(2 \right)}^{2} + 2 \log{\left(2 \right)} \log{\left(5 \right)} + 2 \log{\left(2 \right)} \log{\left(10 \right)}} + \frac{\log{\left(5 \right)}}{- \log{\left(5 \right)} \log{\left(10 \right)} - \log{\left(2 \right)}^{2} + \log{\left(2 \right)} \log{\left(5 \right)} + \log{\left(2 \right)} \log{\left(10 \right)}} - \frac{10 \log{\left(5 \right)}}{- 2 \log{\left(5 \right)} \log{\left(10 \right)} - 2 \log{\left(2 \right)}^{2} + 2 \log{\left(2 \right)} \log{\left(5 \right)} + 2 \log{\left(2 \right)} \log{\left(10 \right)}} - \frac{76 \log{\left(2 \right)}}{- \log{\left(5 \right)} \log{\left(10 \right)} - \log{\left(2 \right)}^{2} + \log{\left(2 \right)} \log{\left(5 \right)} + \log{\left(2 \right)} \log{\left(10 \right)}} - \frac{375 \log{\left(10 \right)}}{- 2 \log{\left(5 \right)} \log{\left(10 \right)} - 2 \log{\left(2 \right)}^{2} + 2 \log{\left(2 \right)} \log{\left(5 \right)} + 2 \log{\left(2 \right)} \log{\left(10 \right)}}$$
log(5)/(-log(2)^2 + log(2)*log(5) + log(2)*log(10) - log(5)*log(10)) - 375*log(10)/(-2*log(2)^2 - 2*log(5)*log(10) + 2*log(2)*log(5) + 2*log(2)*log(10)) - 76*log(2)/(-log(2)^2 + log(2)*log(5) + log(2)*log(10) - log(5)*log(10)) - 10*log(5)/(-2*log(2)^2 - 2*log(5)*log(10) + 2*log(2)*log(5) + 2*log(2)*log(10)) + 75*log(10)/(-log(2)^2 + log(2)*log(5) + log(2)*log(10) - log(5)*log(10)) + 385*log(2)/(-2*log(2)^2 - 2*log(5)*log(10) + 2*log(2)*log(5) + 2*log(2)*log(10))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.