Sr Examen
Integral de 1/(1.4-((3-x^2)/(2+2x^2))) dx
Solución
Ha introducido
[src]
229 ---- 1000 / | | 1 | ------------ dx | 2 | 7 3 - x | - - -------- | 5 2 | 2 + 2*x | / -229 ----- 1000
$$\int\limits_{- \frac{229}{1000}}^{\frac{229}{1000}} \frac{1}{- \frac{3 - x^{2}}{2 x^{2} + 2} + \frac{7}{5}}\, dx$$
Integral(1/(7/5 - (3 - x^2)/(2 + 2*x^2)), (x, -229/1000, 229/1000))
Respuesta (Indefinida)
[src]
// ____ / ____\ \
||-\/ 19 *acoth\x*\/ 19 / 2 |
||------------------------ for x > 1/19|
|| 19 |
200*|< |
|| ____ / ____\ |
/ ||-\/ 19 *atanh\x*\/ 19 / 2 |
| ||------------------------ for x < 1/19|
| 1 10*x \\ 19 /
| ------------ dx = C + ---- + ----------------------------------------------
| 2 19 19
| 7 3 - x
| - - --------
| 5 2
| 2 + 2*x
|
/
$$\int \frac{1}{- \frac{3 - x^{2}}{2 x^{2} + 2} + \frac{7}{5}}\, dx = C + \frac{10 x}{19} + \frac{200 \left(\begin{cases} - \frac{\sqrt{19} \operatorname{acoth}{\left(\sqrt{19} x \right)}}{19} & \text{for}\: x^{2} > \frac{1}{19} \\- \frac{\sqrt{19} \operatorname{atanh}{\left(\sqrt{19} x \right)}}{19} & \text{for}\: x^{2} < \frac{1}{19} \end{cases}\right)}{19}$$
Gráfica
Respuesta
[src]
/ / ____\\ / ____\ / / ____\\ / ____\
____ | |229 \/ 19 || ____ |229 \/ 19 | ____ | | 229 \/ 19 || ____ | 229 \/ 19 |
100*\/ 19 *|pi*I + log|---- + ------|| 100*\/ 19 *log|---- + ------| 100*\/ 19 *|pi*I + log|- ---- + ------|| 100*\/ 19 *log|- ---- + ------|
229 \ \1000 19 // \1000 19 / \ \ 1000 19 // \ 1000 19 /
--- - -------------------------------------- - ----------------------------- + ---------------------------------------- + -------------------------------
950 361 361 361 361
$$\frac{100 \sqrt{19} \log{\left(- \frac{229}{1000} + \frac{\sqrt{19}}{19} \right)}}{361} + \frac{229}{950} - \frac{100 \sqrt{19} \log{\left(\frac{229}{1000} + \frac{\sqrt{19}}{19} \right)}}{361} - \frac{100 \sqrt{19} \left(\log{\left(\frac{229}{1000} + \frac{\sqrt{19}}{19} \right)} + i \pi\right)}{361} + \frac{100 \sqrt{19} \left(\log{\left(- \frac{229}{1000} + \frac{\sqrt{19}}{19} \right)} + i \pi\right)}{361}$$
=
=
/ / ____\\ / ____\ / / ____\\ / ____\
____ | |229 \/ 19 || ____ |229 \/ 19 | ____ | | 229 \/ 19 || ____ | 229 \/ 19 |
100*\/ 19 *|pi*I + log|---- + ------|| 100*\/ 19 *log|---- + ------| 100*\/ 19 *|pi*I + log|- ---- + ------|| 100*\/ 19 *log|- ---- + ------|
229 \ \1000 19 // \1000 19 / \ \ 1000 19 // \ 1000 19 /
--- - -------------------------------------- - ----------------------------- + ---------------------------------------- + -------------------------------
950 361 361 361 361
$$\frac{100 \sqrt{19} \log{\left(- \frac{229}{1000} + \frac{\sqrt{19}}{19} \right)}}{361} + \frac{229}{950} - \frac{100 \sqrt{19} \log{\left(\frac{229}{1000} + \frac{\sqrt{19}}{19} \right)}}{361} - \frac{100 \sqrt{19} \left(\log{\left(\frac{229}{1000} + \frac{\sqrt{19}}{19} \right)} + i \pi\right)}{361} + \frac{100 \sqrt{19} \left(\log{\left(- \frac{229}{1000} + \frac{\sqrt{19}}{19} \right)} + i \pi\right)}{361}$$
229/950 - 100*sqrt(19)*(pi*i + log(229/1000 + sqrt(19)/19))/361 - 100*sqrt(19)*log(229/1000 + sqrt(19)/19)/361 + 100*sqrt(19)*(pi*i + log(-229/1000 + sqrt(19)/19))/361 + 100*sqrt(19)*log(-229/1000 + sqrt(19)/19)/361
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.