Sr Examen
Integral de (x^2-8)/(x^2-3) dx
Solución
Ha introducido
[src]
1 / | | 2 | x - 8 | ------ dx | 2 | x - 3 | / 0
$$\int\limits_{0}^{1} \frac{x^{2} - 8}{x^{2} - 3}\, dx$$
Integral((x^2 - 8)/(x^2 - 3), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___\ \
|| ___ |x*\/ 3 | |
/ ||-\/ 3 *acoth|-------| |
| || \ 3 / 2 |
| 2 ||---------------------- for x > 3|
| x - 8 || 3 |
| ------ dx = C + x - 5*|< |
| 2 || / ___\ |
| x - 3 || ___ |x*\/ 3 | |
| ||-\/ 3 *atanh|-------| |
/ || \ 3 / 2 |
||---------------------- for x < 3|
\\ 3 /
$$\int \frac{x^{2} - 8}{x^{2} - 3}\, dx = C + x - 5 \left(\begin{cases} - \frac{\sqrt{3} \operatorname{acoth}{\left(\frac{\sqrt{3} x}{3} \right)}}{3} & \text{for}\: x^{2} > 3 \\- \frac{\sqrt{3} \operatorname{atanh}{\left(\frac{\sqrt{3} x}{3} \right)}}{3} & \text{for}\: x^{2} < 3 \end{cases}\right)$$
Gráfica
Respuesta
[src]
___ / / ___\\ ___ / ___\ ___ / / ___\\ ___ / ___\
5*\/ 3 *\pi*I + log\-1 + \/ 3 // 5*\/ 3 *log\\/ 3 / 5*\/ 3 *\pi*I + log\\/ 3 // 5*\/ 3 *log\1 + \/ 3 /
1 - -------------------------------- - ------------------ + --------------------------- + ----------------------
6 6 6 6
$$- \frac{5 \sqrt{3} \log{\left(\sqrt{3} \right)}}{6} + 1 + \frac{5 \sqrt{3} \log{\left(1 + \sqrt{3} \right)}}{6} - \frac{5 \sqrt{3} \left(\log{\left(-1 + \sqrt{3} \right)} + i \pi\right)}{6} + \frac{5 \sqrt{3} \left(\log{\left(\sqrt{3} \right)} + i \pi\right)}{6}$$
=
=
___ / / ___\\ ___ / ___\ ___ / / ___\\ ___ / ___\
5*\/ 3 *\pi*I + log\-1 + \/ 3 // 5*\/ 3 *log\\/ 3 / 5*\/ 3 *\pi*I + log\\/ 3 // 5*\/ 3 *log\1 + \/ 3 /
1 - -------------------------------- - ------------------ + --------------------------- + ----------------------
6 6 6 6
$$- \frac{5 \sqrt{3} \log{\left(\sqrt{3} \right)}}{6} + 1 + \frac{5 \sqrt{3} \log{\left(1 + \sqrt{3} \right)}}{6} - \frac{5 \sqrt{3} \left(\log{\left(-1 + \sqrt{3} \right)} + i \pi\right)}{6} + \frac{5 \sqrt{3} \left(\log{\left(\sqrt{3} \right)} + i \pi\right)}{6}$$
1 - 5*sqrt(3)*(pi*i + log(-1 + sqrt(3)))/6 - 5*sqrt(3)*log(sqrt(3))/6 + 5*sqrt(3)*(pi*i + log(sqrt(3)))/6 + 5*sqrt(3)*log(1 + sqrt(3))/6
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.