Sr Examen
Integral de (6x^2)/(x-1*x^2+3x+2) dx
Solución
Ha introducido
[src]
1 / | | 2 | 6*x | ---------------- dx | 2 | x - x + 3*x + 2 | / 0
$$\int\limits_{0}^{1} \frac{6 x^{2}}{\left(3 x + \left(- x^{2} + x\right)\right) + 2}\, dx$$
Integral((6*x^2)/(x - x^2 + 3*x + 2), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___ \ \
|| ___ |\/ 6 *(-2 + x)| |
/ ||-\/ 6 *acoth|--------------| |
| || \ 6 / 2 |
| 2 ||----------------------------- for (-2 + x) > 6|
| 6*x || 6 | / 2 \
| ---------------- dx = C - 60*|< | - 12*log\-2 + x - 4*x/ - 6*x
| 2 || / ___ \ |
| x - x + 3*x + 2 || ___ |\/ 6 *(-2 + x)| |
| ||-\/ 6 *atanh|--------------| |
/ || \ 6 / 2 |
||----------------------------- for (-2 + x) < 6|
\\ 6 /
$$\int \frac{6 x^{2}}{\left(3 x + \left(- x^{2} + x\right)\right) + 2}\, dx = C - 6 x - 60 \left(\begin{cases} - \frac{\sqrt{6} \operatorname{acoth}{\left(\frac{\sqrt{6} \left(x - 2\right)}{6} \right)}}{6} & \text{for}\: \left(x - 2\right)^{2} > 6 \\- \frac{\sqrt{6} \operatorname{atanh}{\left(\frac{\sqrt{6} \left(x - 2\right)}{6} \right)}}{6} & \text{for}\: \left(x - 2\right)^{2} < 6 \end{cases}\right) - 12 \log{\left(x^{2} - 4 x - 2 \right)}$$
Gráfica
Respuesta
[src]
/ ___\ / ___\ / ___\ / ___\
| 5*\/ 6 | / ___\ | 5*\/ 6 | / / ___\\ | 5*\/ 6 | / ___\ | 5*\/ 6 | / / ___\\
-6 - 6*|2 - -------|*log\-1 + \/ 6 / - 6*|2 + -------|*\pi*I + log\1 + \/ 6 // + 6*|2 - -------|*log\-2 + \/ 6 / + 6*|2 + -------|*\pi*I + log\2 + \/ 6 //
\ 6 / \ 6 / \ 6 / \ 6 /
$$-6 - 6 \left(2 - \frac{5 \sqrt{6}}{6}\right) \log{\left(-1 + \sqrt{6} \right)} + 6 \left(2 - \frac{5 \sqrt{6}}{6}\right) \log{\left(-2 + \sqrt{6} \right)} - 6 \left(2 + \frac{5 \sqrt{6}}{6}\right) \left(\log{\left(1 + \sqrt{6} \right)} + i \pi\right) + 6 \left(2 + \frac{5 \sqrt{6}}{6}\right) \left(\log{\left(2 + \sqrt{6} \right)} + i \pi\right)$$
=
=
/ ___\ / ___\ / ___\ / ___\
| 5*\/ 6 | / ___\ | 5*\/ 6 | / / ___\\ | 5*\/ 6 | / ___\ | 5*\/ 6 | / / ___\\
-6 - 6*|2 - -------|*log\-1 + \/ 6 / - 6*|2 + -------|*\pi*I + log\1 + \/ 6 // + 6*|2 - -------|*log\-2 + \/ 6 / + 6*|2 + -------|*\pi*I + log\2 + \/ 6 //
\ 6 / \ 6 / \ 6 / \ 6 /
$$-6 - 6 \left(2 - \frac{5 \sqrt{6}}{6}\right) \log{\left(-1 + \sqrt{6} \right)} + 6 \left(2 - \frac{5 \sqrt{6}}{6}\right) \log{\left(-2 + \sqrt{6} \right)} - 6 \left(2 + \frac{5 \sqrt{6}}{6}\right) \left(\log{\left(1 + \sqrt{6} \right)} + i \pi\right) + 6 \left(2 + \frac{5 \sqrt{6}}{6}\right) \left(\log{\left(2 + \sqrt{6} \right)} + i \pi\right)$$
-6 - 6*(2 - 5*sqrt(6)/6)*log(-1 + sqrt(6)) - 6*(2 + 5*sqrt(6)/6)*(pi*i + log(1 + sqrt(6))) + 6*(2 - 5*sqrt(6)/6)*log(-2 + sqrt(6)) + 6*(2 + 5*sqrt(6)/6)*(pi*i + log(2 + sqrt(6)))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.