Sr Examen
Integral de 1/(4x+5-5x^2) dx
Solución
Ha introducido
[src]
1 / | | 1 | -------------- dx | 2 | 4*x + 5 - 5*x | / 0
$$\int\limits_{0}^{1} \frac{1}{- 5 x^{2} + \left(4 x + 5\right)}\, dx$$
Integral(1/(4*x + 5 - 5*x^2), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ____ \ \
|| ____ |5*\/ 29 *(-2/5 + x)| |
||-\/ 29 *acoth|-------------------| |
/ || \ 29 / 2 29|
| ||----------------------------------- for (-2/5 + x) > --|
| 1 || 145 25|
| -------------- dx = C - 5*|< |
| 2 || / ____ \ |
| 4*x + 5 - 5*x || ____ |5*\/ 29 *(-2/5 + x)| |
| ||-\/ 29 *atanh|-------------------| |
/ || \ 29 / 2 29|
||----------------------------------- for (-2/5 + x) < --|
\\ 145 25/
$$\int \frac{1}{- 5 x^{2} + \left(4 x + 5\right)}\, dx = C - 5 \left(\begin{cases} - \frac{\sqrt{29} \operatorname{acoth}{\left(\frac{5 \sqrt{29} \left(x - \frac{2}{5}\right)}{29} \right)}}{145} & \text{for}\: \left(x - \frac{2}{5}\right)^{2} > \frac{29}{25} \\- \frac{\sqrt{29} \operatorname{atanh}{\left(\frac{5 \sqrt{29} \left(x - \frac{2}{5}\right)}{29} \right)}}{145} & \text{for}\: \left(x - \frac{2}{5}\right)^{2} < \frac{29}{25} \end{cases}\right)$$
Gráfica
Respuesta
[src]
/ / ____\\ / ____\ / / ____\\ / ____\
____ | | 3 \/ 29 || ____ | 2 \/ 29 | ____ | |2 \/ 29 || ____ |3 \/ 29 |
\/ 29 *|pi*I + log|- - + ------|| \/ 29 *log|- - + ------| \/ 29 *|pi*I + log|- + ------|| \/ 29 *log|- + ------|
\ \ 5 5 // \ 5 5 / \ \5 5 // \5 5 /
- --------------------------------- - ------------------------ + ------------------------------- + ----------------------
58 58 58 58
$$- \frac{\sqrt{29} \log{\left(- \frac{2}{5} + \frac{\sqrt{29}}{5} \right)}}{58} + \frac{\sqrt{29} \log{\left(\frac{3}{5} + \frac{\sqrt{29}}{5} \right)}}{58} - \frac{\sqrt{29} \left(\log{\left(- \frac{3}{5} + \frac{\sqrt{29}}{5} \right)} + i \pi\right)}{58} + \frac{\sqrt{29} \left(\log{\left(\frac{2}{5} + \frac{\sqrt{29}}{5} \right)} + i \pi\right)}{58}$$
=
=
/ / ____\\ / ____\ / / ____\\ / ____\
____ | | 3 \/ 29 || ____ | 2 \/ 29 | ____ | |2 \/ 29 || ____ |3 \/ 29 |
\/ 29 *|pi*I + log|- - + ------|| \/ 29 *log|- - + ------| \/ 29 *|pi*I + log|- + ------|| \/ 29 *log|- + ------|
\ \ 5 5 // \ 5 5 / \ \5 5 // \5 5 /
- --------------------------------- - ------------------------ + ------------------------------- + ----------------------
58 58 58 58
$$- \frac{\sqrt{29} \log{\left(- \frac{2}{5} + \frac{\sqrt{29}}{5} \right)}}{58} + \frac{\sqrt{29} \log{\left(\frac{3}{5} + \frac{\sqrt{29}}{5} \right)}}{58} - \frac{\sqrt{29} \left(\log{\left(- \frac{3}{5} + \frac{\sqrt{29}}{5} \right)} + i \pi\right)}{58} + \frac{\sqrt{29} \left(\log{\left(\frac{2}{5} + \frac{\sqrt{29}}{5} \right)} + i \pi\right)}{58}$$
-sqrt(29)*(pi*i + log(-3/5 + sqrt(29)/5))/58 - sqrt(29)*log(-2/5 + sqrt(29)/5)/58 + sqrt(29)*(pi*i + log(2/5 + sqrt(29)/5))/58 + sqrt(29)*log(3/5 + sqrt(29)/5)/58
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.