Sr Examen
Integral de (x^2+2X^3-5x)/(4-2x^2+x) dx
Solución
Ha introducido
[src]
1 / | | 2 3 | x + 2*x - 5*x | --------------- dx | 2 | 4 - 2*x + x | / 0
$$\int\limits_{0}^{1} \frac{- 5 x + \left(2 x^{3} + x^{2}\right)}{x + \left(4 - 2 x^{2}\right)}\, dx$$
Integral((x^2 + 2*x^3 - 5*x)/(4 - 2*x^2 + x), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ____ \ \
|| ____ |4*\/ 33 *(-1/4 + x)| |
/ ||-\/ 33 *acoth|-------------------| |
| || \ 33 / 2 33|
| 2 3 ||----------------------------------- for (-1/4 + x) > --| 2
| x + 2*x - 5*x || 132 16| x
| --------------- dx = C - x - 32*|< | - --
| 2 || / ____ \ | 2
| 4 - 2*x + x || ____ |4*\/ 33 *(-1/4 + x)| |
| ||-\/ 33 *atanh|-------------------| |
/ || \ 33 / 2 33|
||----------------------------------- for (-1/4 + x) < --|
\\ 132 16/
$$\int \frac{- 5 x + \left(2 x^{3} + x^{2}\right)}{x + \left(4 - 2 x^{2}\right)}\, dx = C - \frac{x^{2}}{2} - x - 32 \left(\begin{cases} - \frac{\sqrt{33} \operatorname{acoth}{\left(\frac{4 \sqrt{33} \left(x - \frac{1}{4}\right)}{33} \right)}}{132} & \text{for}\: \left(x - \frac{1}{4}\right)^{2} > \frac{33}{16} \\- \frac{\sqrt{33} \operatorname{atanh}{\left(\frac{4 \sqrt{33} \left(x - \frac{1}{4}\right)}{33} \right)}}{132} & \text{for}\: \left(x - \frac{1}{4}\right)^{2} < \frac{33}{16} \end{cases}\right)$$
Gráfica
Respuesta
[src]
/ / ____\\ / ____\ / / ____\\ / ____\
____ | | 3 \/ 33 || ____ | 1 \/ 33 | ____ | |1 \/ 33 || ____ |3 \/ 33 |
4*\/ 33 *|pi*I + log|- - + ------|| 4*\/ 33 *log|- - + ------| 4*\/ 33 *|pi*I + log|- + ------|| 4*\/ 33 *log|- + ------|
3 \ \ 4 4 // \ 4 4 / \ \4 4 // \4 4 /
- - - ----------------------------------- - -------------------------- + --------------------------------- + ------------------------
2 33 33 33 33
$$- \frac{3}{2} - \frac{4 \sqrt{33} \log{\left(- \frac{1}{4} + \frac{\sqrt{33}}{4} \right)}}{33} + \frac{4 \sqrt{33} \log{\left(\frac{3}{4} + \frac{\sqrt{33}}{4} \right)}}{33} - \frac{4 \sqrt{33} \left(\log{\left(- \frac{3}{4} + \frac{\sqrt{33}}{4} \right)} + i \pi\right)}{33} + \frac{4 \sqrt{33} \left(\log{\left(\frac{1}{4} + \frac{\sqrt{33}}{4} \right)} + i \pi\right)}{33}$$
=
=
/ / ____\\ / ____\ / / ____\\ / ____\
____ | | 3 \/ 33 || ____ | 1 \/ 33 | ____ | |1 \/ 33 || ____ |3 \/ 33 |
4*\/ 33 *|pi*I + log|- - + ------|| 4*\/ 33 *log|- - + ------| 4*\/ 33 *|pi*I + log|- + ------|| 4*\/ 33 *log|- + ------|
3 \ \ 4 4 // \ 4 4 / \ \4 4 // \4 4 /
- - - ----------------------------------- - -------------------------- + --------------------------------- + ------------------------
2 33 33 33 33
$$- \frac{3}{2} - \frac{4 \sqrt{33} \log{\left(- \frac{1}{4} + \frac{\sqrt{33}}{4} \right)}}{33} + \frac{4 \sqrt{33} \log{\left(\frac{3}{4} + \frac{\sqrt{33}}{4} \right)}}{33} - \frac{4 \sqrt{33} \left(\log{\left(- \frac{3}{4} + \frac{\sqrt{33}}{4} \right)} + i \pi\right)}{33} + \frac{4 \sqrt{33} \left(\log{\left(\frac{1}{4} + \frac{\sqrt{33}}{4} \right)} + i \pi\right)}{33}$$
-3/2 - 4*sqrt(33)*(pi*i + log(-3/4 + sqrt(33)/4))/33 - 4*sqrt(33)*log(-1/4 + sqrt(33)/4)/33 + 4*sqrt(33)*(pi*i + log(1/4 + sqrt(33)/4))/33 + 4*sqrt(33)*log(3/4 + sqrt(33)/4)/33
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.