Sr Examen
Integral de x^4/(x^3-3*x^2+2) dx
Solución
Ha introducido
[src]
1 / | | 4 | x | ------------- dx | 3 2 | x - 3*x + 2 | / 0
$$\int\limits_{0}^{1} \frac{x^{4}}{\left(x^{3} - 3 x^{2}\right) + 2}\, dx$$
Integral(x^4/(x^3 - 3*x^2 + 2), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___ \ \
|| ___ |\/ 3 *(-1 + x)| |
/ ||-\/ 3 *acoth|--------------| |
| || \ 3 / 2 |
| 4 2 ||----------------------------- for (-1 + x) > 3| / 2 \
| x x || 3 | log(-1 + x) 14*log\-2 + x - 2*x/
| ------------- dx = C + -- + 3*x + 16*|< | - ----------- + ---------------------
| 3 2 2 || / ___ \ | 3 3
| x - 3*x + 2 || ___ |\/ 3 *(-1 + x)| |
| ||-\/ 3 *atanh|--------------| |
/ || \ 3 / 2 |
||----------------------------- for (-1 + x) < 3|
\\ 3 /
$$\int \frac{x^{4}}{\left(x^{3} - 3 x^{2}\right) + 2}\, dx = C + \frac{x^{2}}{2} + 3 x + 16 \left(\begin{cases} - \frac{\sqrt{3} \operatorname{acoth}{\left(\frac{\sqrt{3} \left(x - 1\right)}{3} \right)}}{3} & \text{for}\: \left(x - 1\right)^{2} > 3 \\- \frac{\sqrt{3} \operatorname{atanh}{\left(\frac{\sqrt{3} \left(x - 1\right)}{3} \right)}}{3} & \text{for}\: \left(x - 1\right)^{2} < 3 \end{cases}\right) - \frac{\log{\left(x - 1 \right)}}{3} + \frac{14 \log{\left(x^{2} - 2 x - 2 \right)}}{3}$$
Gráfica
Respuesta
[src]
/ / 2\\
| | / ___\ ||
| | |14 8*\/ 3 | ||
/ ___\ | | ___ 45*|-- + -------| ||
|14 8*\/ 3 | | | 463 129*\/ 3 \3 3 / || pi*I
oo - |-- + -------|*|pi*I + log|- --- - --------- + ------------------|| + ----
\3 3 / \ \ 22 11 88 // 3
$$\infty - \left(\frac{8 \sqrt{3}}{3} + \frac{14}{3}\right) \left(\log{\left(- \frac{463}{22} - \frac{129 \sqrt{3}}{11} + \frac{45 \left(\frac{8 \sqrt{3}}{3} + \frac{14}{3}\right)^{2}}{88} \right)} + i \pi\right) + \frac{i \pi}{3}$$
=
=
/ / 2\\
| | / ___\ ||
| | |14 8*\/ 3 | ||
/ ___\ | | ___ 45*|-- + -------| ||
|14 8*\/ 3 | | | 463 129*\/ 3 \3 3 / || pi*I
oo - |-- + -------|*|pi*I + log|- --- - --------- + ------------------|| + ----
\3 3 / \ \ 22 11 88 // 3
$$\infty - \left(\frac{8 \sqrt{3}}{3} + \frac{14}{3}\right) \left(\log{\left(- \frac{463}{22} - \frac{129 \sqrt{3}}{11} + \frac{45 \left(\frac{8 \sqrt{3}}{3} + \frac{14}{3}\right)^{2}}{88} \right)} + i \pi\right) + \frac{i \pi}{3}$$
oo - (14/3 + 8*sqrt(3)/3)*(pi*i + log(-463/22 - 129*sqrt(3)/11 + 45*(14/3 + 8*sqrt(3)/3)^2/88)) + pi*i/3
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.