Sr Examen
Integral de (x-1)/((x+2)*(x^(2)-2x+4)) dx
Solución
Ha introducido
[src]
1 / | | x - 1 | ---------------------- dx | / 2 \ | (x + 2)*\x - 2*x + 4/ | / 0
$$\int\limits_{0}^{1} \frac{x - 1}{\left(x + 2\right) \left(\left(x^{2} - 2 x\right) + 4\right)}\, dx$$
Integral((x - 1)/(((x + 2)*(x^2 - 2*x + 4))), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ___ \ / ___ |\/ 3 *(-1 + x)| | / 2 \ \/ 3 *atan|--------------| | x - 1 log(2 + x) log\4 + x - 2*x/ \ 3 / | ---------------------- dx = C - ---------- + ----------------- + -------------------------- | / 2 \ 4 8 12 | (x + 2)*\x - 2*x + 4/ | /
$$\int \frac{x - 1}{\left(x + 2\right) \left(\left(x^{2} - 2 x\right) + 4\right)}\, dx = C - \frac{\log{\left(x + 2 \right)}}{4} + \frac{\log{\left(x^{2} - 2 x + 4 \right)}}{8} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(x - 1\right)}{3} \right)}}{12}$$
Gráfica
Respuesta
[src]
___
log(3) log(4) log(2) pi*\/ 3
- ------ - ------ + ------ + --------
8 8 4 72
$$- \frac{\log{\left(4 \right)}}{8} - \frac{\log{\left(3 \right)}}{8} + \frac{\sqrt{3} \pi}{72} + \frac{\log{\left(2 \right)}}{4}$$
=
=
___
log(3) log(4) log(2) pi*\/ 3
- ------ - ------ + ------ + --------
8 8 4 72
$$- \frac{\log{\left(4 \right)}}{8} - \frac{\log{\left(3 \right)}}{8} + \frac{\sqrt{3} \pi}{72} + \frac{\log{\left(2 \right)}}{4}$$
-log(3)/8 - log(4)/8 + log(2)/4 + pi*sqrt(3)/72
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.