Sr Examen
Integral de (4^(x+2)-2^(3x+3)-4+16^x+2^x)/(4^x) dx
Solución
Ha introducido
[src]
2 / | | x + 2 3*x + 3 x x | 4 - 2 - 4 + 16 + 2 | -------------------------------- dx | x | 4 | / 0
$$\int\limits_{0}^{2} \frac{2^{x} + \left(16^{x} + \left(\left(- 2^{3 x + 3} + 4^{x + 2}\right) - 4\right)\right)}{4^{x}}\, dx$$
Integral((4^(x + 2) - 2^(3*x + 3) - 4 + 16^x + 2^x)/4^x, (x, 0, 2))
Gráfica
Respuesta
[src]
log(4) 2*log(4) -2*log(4) -log(4)
------ -------- --------- --------
log(2) 3 log(2) 3 log(2) 3 log(2) 3
13 4 *log (2) - 16*4 *log (2) - 2*4 *log (2) + 4*4 *log (2)
32 + -------- + -----------------------------------------------------------------------------------
2*log(2) 4
2*log (2)
$$\frac{- 16 \cdot 4^{\frac{2 \log{\left(4 \right)}}{\log{\left(2 \right)}}} \log{\left(2 \right)}^{3} - \frac{2 \log{\left(2 \right)}^{3}}{4^{\frac{2 \log{\left(4 \right)}}{\log{\left(2 \right)}}}} + \frac{4 \log{\left(2 \right)}^{3}}{4^{\frac{\log{\left(4 \right)}}{\log{\left(2 \right)}}}} + 4^{\frac{\log{\left(4 \right)}}{\log{\left(2 \right)}}} \log{\left(2 \right)}^{3}}{2 \log{\left(2 \right)}^{4}} + \frac{13}{2 \log{\left(2 \right)}} + 32$$
=
=
log(4) 2*log(4) -2*log(4) -log(4)
------ -------- --------- --------
log(2) 3 log(2) 3 log(2) 3 log(2) 3
13 4 *log (2) - 16*4 *log (2) - 2*4 *log (2) + 4*4 *log (2)
32 + -------- + -----------------------------------------------------------------------------------
2*log(2) 4
2*log (2)
$$\frac{- 16 \cdot 4^{\frac{2 \log{\left(4 \right)}}{\log{\left(2 \right)}}} \log{\left(2 \right)}^{3} - \frac{2 \log{\left(2 \right)}^{3}}{4^{\frac{2 \log{\left(4 \right)}}{\log{\left(2 \right)}}}} + \frac{4 \log{\left(2 \right)}^{3}}{4^{\frac{\log{\left(4 \right)}}{\log{\left(2 \right)}}}} + 4^{\frac{\log{\left(4 \right)}}{\log{\left(2 \right)}}} \log{\left(2 \right)}^{3}}{2 \log{\left(2 \right)}^{4}} + \frac{13}{2 \log{\left(2 \right)}} + 32$$
32 + 13/(2*log(2)) + (4^(log(4)/log(2))*log(2)^3 - 16*4^(2*log(4)/log(2))*log(2)^3 - 2*4^(-2*log(4)/log(2))*log(2)^3 + 4*4^(-log(4)/log(2))*log(2)^3)/(2*log(2)^4)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.