Sr Examen
Integral de (2x^2-5)/(x^4-5x^2+6) dx
Solución
Ha introducido
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0 / | | 2 | 2*x - 5 | ------------- dx | 4 2 | x - 5*x + 6 | / 0
$$\int\limits_{0}^{0} \frac{2 x^{2} - 5}{\left(x^{4} - 5 x^{2}\right) + 6}\, dx$$
Integral((2*x^2 - 5)/(x^4 - 5*x^2 + 6), (x, 0, 0))
Respuesta (Indefinida)
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// / ___\ \ // / ___\ \
|| ___ |x*\/ 2 | | || ___ |x*\/ 3 | |
/ ||-\/ 2 *acoth|-------| | ||-\/ 3 *acoth|-------| |
| || \ 2 / 2 | || \ 3 / 2 |
| 2 ||---------------------- for x > 2| ||---------------------- for x > 3|
| 2*x - 5 || 2 | || 3 |
| ------------- dx = C + |< | + |< |
| 4 2 || / ___\ | || / ___\ |
| x - 5*x + 6 || ___ |x*\/ 2 | | || ___ |x*\/ 3 | |
| ||-\/ 2 *atanh|-------| | ||-\/ 3 *atanh|-------| |
/ || \ 2 / 2 | || \ 3 / 2 |
||---------------------- for x < 2| ||---------------------- for x < 3|
\\ 2 / \\ 3 /
$$\int \frac{2 x^{2} - 5}{\left(x^{4} - 5 x^{2}\right) + 6}\, dx = C + \begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2} x}{2} \right)}}{2} & \text{for}\: x^{2} > 2 \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2} x}{2} \right)}}{2} & \text{for}\: x^{2} < 2 \end{cases} + \begin{cases} - \frac{\sqrt{3} \operatorname{acoth}{\left(\frac{\sqrt{3} x}{3} \right)}}{3} & \text{for}\: x^{2} > 3 \\- \frac{\sqrt{3} \operatorname{atanh}{\left(\frac{\sqrt{3} x}{3} \right)}}{3} & \text{for}\: x^{2} < 3 \end{cases}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.