Sr Examen
Integral de (x-1)*5^(x-2)/6^x dx
Solución
Ha introducido
[src]
3 / | | x - 2 | (x - 1)*5 | -------------- dx | x | 6 | / 0
$$\int\limits_{0}^{3} \frac{5^{x - 2} \left(x - 1\right)}{6^{x}}\, dx$$
Integral(((x - 1)*5^(x - 2))/6^x, (x, 0, 3))
Respuesta (Indefinida)
[src]
/ | | x - 2 x x x x | (x - 1)*5 5 5 x*5 *log(6) x*5 *log(5) | -------------- dx = C - -------------------------- - ------------------------------------------------- - ------------------------------------------------- + ------------------------------------------------- | x / x x \ / x 2 x 2 x \ / x 2 x 2 x \ / x 2 x 2 x \ | 6 25*\6 *log(5) - 6 *log(6)/ 25*\6 *log (5) + 6 *log (6) - 2*6 *log(5)*log(6)/ 25*\6 *log (5) + 6 *log (6) - 2*6 *log(5)*log(6)/ 25*\6 *log (5) + 6 *log (6) - 2*6 *log(5)*log(6)/ | /
$$\int \frac{5^{x - 2} \left(x - 1\right)}{6^{x}}\, dx = - \frac{5^{x} x \log{\left(6 \right)}}{25 \left(- 2 \cdot 6^{x} \log{\left(5 \right)} \log{\left(6 \right)} + 6^{x} \log{\left(5 \right)}^{2} + 6^{x} \log{\left(6 \right)}^{2}\right)} + \frac{5^{x} x \log{\left(5 \right)}}{25 \left(- 2 \cdot 6^{x} \log{\left(5 \right)} \log{\left(6 \right)} + 6^{x} \log{\left(5 \right)}^{2} + 6^{x} \log{\left(6 \right)}^{2}\right)} - \frac{5^{x}}{25 \left(- 2 \cdot 6^{x} \log{\left(5 \right)} \log{\left(6 \right)} + 6^{x} \log{\left(5 \right)}^{2} + 6^{x} \log{\left(6 \right)}^{2}\right)} - \frac{5^{x}}{25 \left(- 6^{x} \log{\left(6 \right)} + 6^{x} \log{\left(5 \right)}\right)} + C$$
Gráfica
Respuesta
[src]
1 125 log(5) log(6) 250*log(6) 250*log(5)
------------------------------------------ - ------------------------------------------------- + ------------------------------------------ - ------------------------------------------ - ------------------------------------------------- + -------------------------------------------------
2 2 2 2 2 2 2 2 2 2 2 2
25*log (5) + 25*log (6) - 50*log(5)*log(6) 5400*log (5) + 5400*log (6) - 10800*log(5)*log(6) 25*log (5) + 25*log (6) - 50*log(5)*log(6) 25*log (5) + 25*log (6) - 50*log(5)*log(6) 5400*log (5) + 5400*log (6) - 10800*log(5)*log(6) 5400*log (5) + 5400*log (6) - 10800*log(5)*log(6)
$$- \frac{250 \log{\left(6 \right)}}{- 10800 \log{\left(5 \right)} \log{\left(6 \right)} + 5400 \log{\left(5 \right)}^{2} + 5400 \log{\left(6 \right)}^{2}} - \frac{\log{\left(6 \right)}}{- 50 \log{\left(5 \right)} \log{\left(6 \right)} + 25 \log{\left(5 \right)}^{2} + 25 \log{\left(6 \right)}^{2}} - \frac{125}{- 10800 \log{\left(5 \right)} \log{\left(6 \right)} + 5400 \log{\left(5 \right)}^{2} + 5400 \log{\left(6 \right)}^{2}} + \frac{1}{- 50 \log{\left(5 \right)} \log{\left(6 \right)} + 25 \log{\left(5 \right)}^{2} + 25 \log{\left(6 \right)}^{2}} + \frac{\log{\left(5 \right)}}{- 50 \log{\left(5 \right)} \log{\left(6 \right)} + 25 \log{\left(5 \right)}^{2} + 25 \log{\left(6 \right)}^{2}} + \frac{250 \log{\left(5 \right)}}{- 10800 \log{\left(5 \right)} \log{\left(6 \right)} + 5400 \log{\left(5 \right)}^{2} + 5400 \log{\left(6 \right)}^{2}}$$
=
=
1 125 log(5) log(6) 250*log(6) 250*log(5)
------------------------------------------ - ------------------------------------------------- + ------------------------------------------ - ------------------------------------------ - ------------------------------------------------- + -------------------------------------------------
2 2 2 2 2 2 2 2 2 2 2 2
25*log (5) + 25*log (6) - 50*log(5)*log(6) 5400*log (5) + 5400*log (6) - 10800*log(5)*log(6) 25*log (5) + 25*log (6) - 50*log(5)*log(6) 25*log (5) + 25*log (6) - 50*log(5)*log(6) 5400*log (5) + 5400*log (6) - 10800*log(5)*log(6) 5400*log (5) + 5400*log (6) - 10800*log(5)*log(6)
$$- \frac{250 \log{\left(6 \right)}}{- 10800 \log{\left(5 \right)} \log{\left(6 \right)} + 5400 \log{\left(5 \right)}^{2} + 5400 \log{\left(6 \right)}^{2}} - \frac{\log{\left(6 \right)}}{- 50 \log{\left(5 \right)} \log{\left(6 \right)} + 25 \log{\left(5 \right)}^{2} + 25 \log{\left(6 \right)}^{2}} - \frac{125}{- 10800 \log{\left(5 \right)} \log{\left(6 \right)} + 5400 \log{\left(5 \right)}^{2} + 5400 \log{\left(6 \right)}^{2}} + \frac{1}{- 50 \log{\left(5 \right)} \log{\left(6 \right)} + 25 \log{\left(5 \right)}^{2} + 25 \log{\left(6 \right)}^{2}} + \frac{\log{\left(5 \right)}}{- 50 \log{\left(5 \right)} \log{\left(6 \right)} + 25 \log{\left(5 \right)}^{2} + 25 \log{\left(6 \right)}^{2}} + \frac{250 \log{\left(5 \right)}}{- 10800 \log{\left(5 \right)} \log{\left(6 \right)} + 5400 \log{\left(5 \right)}^{2} + 5400 \log{\left(6 \right)}^{2}}$$
1/(25*log(5)^2 + 25*log(6)^2 - 50*log(5)*log(6)) - 125/(5400*log(5)^2 + 5400*log(6)^2 - 10800*log(5)*log(6)) + log(5)/(25*log(5)^2 + 25*log(6)^2 - 50*log(5)*log(6)) - log(6)/(25*log(5)^2 + 25*log(6)^2 - 50*log(5)*log(6)) - 250*log(6)/(5400*log(5)^2 + 5400*log(6)^2 - 10800*log(5)*log(6)) + 250*log(5)/(5400*log(5)^2 + 5400*log(6)^2 - 10800*log(5)*log(6))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.