Sr Examen
Integral de -(x^2+3*x-4)/(-x^2+2*x+1) dx
Solución
Ha introducido
[src]
1 / | | 2 | - x - 3*x + 4 | -------------- dx | 2 | - x + 2*x + 1 | / 0
$$\int\limits_{0}^{1} \frac{\left(- x^{2} - 3 x\right) + 4}{\left(- x^{2} + 2 x\right) + 1}\, dx$$
Integral((-x^2 - 3*x + 4)/(-x^2 + 2*x + 1), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___ \ \
|| ___ |\/ 2 *(-1 + x)| |
/ ||-\/ 2 *acoth|--------------| |
| || \ 2 / 2 |
| 2 ||----------------------------- for (-1 + x) > 2| / 2 \
| - x - 3*x + 4 || 2 | 5*log\-1 + x - 2*x/
| -------------- dx = C + x + 2*|< | + --------------------
| 2 || / ___ \ | 2
| - x + 2*x + 1 || ___ |\/ 2 *(-1 + x)| |
| ||-\/ 2 *atanh|--------------| |
/ || \ 2 / 2 |
||----------------------------- for (-1 + x) < 2|
\\ 2 /
$$\int \frac{\left(- x^{2} - 3 x\right) + 4}{\left(- x^{2} + 2 x\right) + 1}\, dx = C + x + 2 \left(\begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2} \left(x - 1\right)}{2} \right)}}{2} & \text{for}\: \left(x - 1\right)^{2} > 2 \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2} \left(x - 1\right)}{2} \right)}}{2} & \text{for}\: \left(x - 1\right)^{2} < 2 \end{cases}\right) + \frac{5 \log{\left(x^{2} - 2 x - 1 \right)}}{2}$$
Gráfica
Respuesta
[src]
/ ___\ / ___\ / ___\ / ___\
|5 \/ 2 | / / ___\\ |5 \/ 2 | / ___\ |5 \/ 2 | / / ___\\ |5 \/ 2 | / ___\
1 + |- + -----|*\pi*I + log\\/ 2 // + |- - -----|*log\\/ 2 / - |- + -----|*\pi*I + log\1 + \/ 2 // - |- - -----|*log\-1 + \/ 2 /
\2 2 / \2 2 / \2 2 / \2 2 /
$$\left(\frac{5}{2} - \frac{\sqrt{2}}{2}\right) \log{\left(\sqrt{2} \right)} + 1 - \left(\frac{5}{2} - \frac{\sqrt{2}}{2}\right) \log{\left(-1 + \sqrt{2} \right)} - \left(\frac{\sqrt{2}}{2} + \frac{5}{2}\right) \left(\log{\left(1 + \sqrt{2} \right)} + i \pi\right) + \left(\frac{\sqrt{2}}{2} + \frac{5}{2}\right) \left(\log{\left(\sqrt{2} \right)} + i \pi\right)$$
=
=
/ ___\ / ___\ / ___\ / ___\
|5 \/ 2 | / / ___\\ |5 \/ 2 | / ___\ |5 \/ 2 | / / ___\\ |5 \/ 2 | / ___\
1 + |- + -----|*\pi*I + log\\/ 2 // + |- - -----|*log\\/ 2 / - |- + -----|*\pi*I + log\1 + \/ 2 // - |- - -----|*log\-1 + \/ 2 /
\2 2 / \2 2 / \2 2 / \2 2 /
$$\left(\frac{5}{2} - \frac{\sqrt{2}}{2}\right) \log{\left(\sqrt{2} \right)} + 1 - \left(\frac{5}{2} - \frac{\sqrt{2}}{2}\right) \log{\left(-1 + \sqrt{2} \right)} - \left(\frac{\sqrt{2}}{2} + \frac{5}{2}\right) \left(\log{\left(1 + \sqrt{2} \right)} + i \pi\right) + \left(\frac{\sqrt{2}}{2} + \frac{5}{2}\right) \left(\log{\left(\sqrt{2} \right)} + i \pi\right)$$
1 + (5/2 + sqrt(2)/2)*(pi*i + log(sqrt(2))) + (5/2 - sqrt(2)/2)*log(sqrt(2)) - (5/2 + sqrt(2)/2)*(pi*i + log(1 + sqrt(2))) - (5/2 - sqrt(2)/2)*log(-1 + sqrt(2))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.