Sr Examen
Integral de (x^2-4x+5)/((x+2)(x^2+4)) dx
Solución
Ha introducido
[src]
1 / | | 2 | x - 4*x + 5 | ---------------- dx | / 2 \ | (x + 2)*\x + 4/ | / 0
$$\int\limits_{0}^{1} \frac{\left(x^{2} - 4 x\right) + 5}{\left(x + 2\right) \left(x^{2} + 4\right)}\, dx$$
Integral((x^2 - 4*x + 5)/(((x + 2)*(x^2 + 4))), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | /x\ | 2 / 2\ 7*atan|-| | x - 4*x + 5 9*log\4 + x / \2/ 17*log(2 + x) | ---------------- dx = C - ------------- - --------- + ------------- | / 2 \ 16 8 8 | (x + 2)*\x + 4/ | /
$$\int \frac{\left(x^{2} - 4 x\right) + 5}{\left(x + 2\right) \left(x^{2} + 4\right)}\, dx = C + \frac{17 \log{\left(x + 2 \right)}}{8} - \frac{9 \log{\left(x^{2} + 4 \right)}}{16} - \frac{7 \operatorname{atan}{\left(\frac{x}{2} \right)}}{8}$$
Gráfica
Respuesta
[src]
17*log(2) 9*log(5) 7*atan(1/2) 9*log(4) 17*log(3)
- --------- - -------- - ----------- + -------- + ---------
8 16 8 16 8
$$- \frac{17 \log{\left(2 \right)}}{8} - \frac{9 \log{\left(5 \right)}}{16} - \frac{7 \operatorname{atan}{\left(\frac{1}{2} \right)}}{8} + \frac{9 \log{\left(4 \right)}}{16} + \frac{17 \log{\left(3 \right)}}{8}$$
=
=
17*log(2) 9*log(5) 7*atan(1/2) 9*log(4) 17*log(3)
- --------- - -------- - ----------- + -------- + ---------
8 16 8 16 8
$$- \frac{17 \log{\left(2 \right)}}{8} - \frac{9 \log{\left(5 \right)}}{16} - \frac{7 \operatorname{atan}{\left(\frac{1}{2} \right)}}{8} + \frac{9 \log{\left(4 \right)}}{16} + \frac{17 \log{\left(3 \right)}}{8}$$
-17*log(2)/8 - 9*log(5)/16 - 7*atan(1/2)/8 + 9*log(4)/16 + 17*log(3)/8
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.