Sr Examen
Integral de (2x-3)/(x^2+2x-7) dx
Solución
Ha introducido
[src]
1 / | | 2*x - 3 | ------------ dx | 2 | x + 2*x - 7 | / 0
$$\int\limits_{0}^{1} \frac{2 x - 3}{\left(x^{2} + 2 x\right) - 7}\, dx$$
Integral((2*x - 3)/(x^2 + 2*x - 7), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___ \ \
|| ___ |\/ 2 *(1 + x)| |
||-\/ 2 *acoth|-------------| |
/ || \ 4 / 2 |
| ||---------------------------- for (1 + x) > 8|
| 2*x - 3 || 4 | / 2 \
| ------------ dx = C - 5*|< | + log\-7 + x + 2*x/
| 2 || / ___ \ |
| x + 2*x - 7 || ___ |\/ 2 *(1 + x)| |
| ||-\/ 2 *atanh|-------------| |
/ || \ 4 / 2 |
||---------------------------- for (1 + x) < 8|
\\ 4 /
$$\int \frac{2 x - 3}{\left(x^{2} + 2 x\right) - 7}\, dx = C - 5 \left(\begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2} \left(x + 1\right)}{4} \right)}}{4} & \text{for}\: \left(x + 1\right)^{2} > 8 \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2} \left(x + 1\right)}{4} \right)}}{4} & \text{for}\: \left(x + 1\right)^{2} < 8 \end{cases}\right) + \log{\left(x^{2} + 2 x - 7 \right)}$$
Gráfica
Respuesta
[src]
/ ___\ / ___\ / ___\ / ___\ | 5*\/ 2 | / / ___\\ | 5*\/ 2 | / ___\ | 5*\/ 2 | / / ___\\ | 5*\/ 2 | / ___\ |1 - -------|*\pi*I + log\-2 + 2*\/ 2 // + |1 + -------|*log\2 + 2*\/ 2 / - |1 - -------|*\pi*I + log\-1 + 2*\/ 2 // - |1 + -------|*log\1 + 2*\/ 2 / \ 8 / \ 8 / \ 8 / \ 8 /
$$- \left(\frac{5 \sqrt{2}}{8} + 1\right) \log{\left(1 + 2 \sqrt{2} \right)} + \left(\frac{5 \sqrt{2}}{8} + 1\right) \log{\left(2 + 2 \sqrt{2} \right)} - \left(1 - \frac{5 \sqrt{2}}{8}\right) \left(\log{\left(-1 + 2 \sqrt{2} \right)} + i \pi\right) + \left(1 - \frac{5 \sqrt{2}}{8}\right) \left(\log{\left(-2 + 2 \sqrt{2} \right)} + i \pi\right)$$
=
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/ ___\ / ___\ / ___\ / ___\ | 5*\/ 2 | / / ___\\ | 5*\/ 2 | / ___\ | 5*\/ 2 | / / ___\\ | 5*\/ 2 | / ___\ |1 - -------|*\pi*I + log\-2 + 2*\/ 2 // + |1 + -------|*log\2 + 2*\/ 2 / - |1 - -------|*\pi*I + log\-1 + 2*\/ 2 // - |1 + -------|*log\1 + 2*\/ 2 / \ 8 / \ 8 / \ 8 / \ 8 /
$$- \left(\frac{5 \sqrt{2}}{8} + 1\right) \log{\left(1 + 2 \sqrt{2} \right)} + \left(\frac{5 \sqrt{2}}{8} + 1\right) \log{\left(2 + 2 \sqrt{2} \right)} - \left(1 - \frac{5 \sqrt{2}}{8}\right) \left(\log{\left(-1 + 2 \sqrt{2} \right)} + i \pi\right) + \left(1 - \frac{5 \sqrt{2}}{8}\right) \left(\log{\left(-2 + 2 \sqrt{2} \right)} + i \pi\right)$$
(1 - 5*sqrt(2)/8)*(pi*i + log(-2 + 2*sqrt(2))) + (1 + 5*sqrt(2)/8)*log(2 + 2*sqrt(2)) - (1 - 5*sqrt(2)/8)*(pi*i + log(-1 + 2*sqrt(2))) - (1 + 5*sqrt(2)/8)*log(1 + 2*sqrt(2))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.