Sr Examen
Integral de (2x+5)/(2x^2-3)^2 dx
Solución
Ha introducido
[src]
1 / | | 2*x + 5 | ----------- dx | 2 | / 2 \ | \2*x - 3/ | / 0
$$\int\limits_{0}^{1} \frac{2 x + 5}{\left(2 x^{2} - 3\right)^{2}}\, dx$$
Integral((2*x + 5)/(2*x^2 - 3)^2, (x, 0, 1))
Gráfica
Respuesta
[src]
/ / ___\\ / ___\ / / ___\\ / ___\
___ | | \/ 6 || ___ |\/ 6 | ___ | |\/ 6 || ___ | \/ 6 |
5*\/ 6 *|pi*I + log|-1 + -----|| 5*\/ 6 *log|-----| 5*\/ 6 *|pi*I + log|-----|| 5*\/ 6 *log|1 + -----|
7 \ \ 2 // \ 2 / \ \ 2 // \ 2 /
- - -------------------------------- - ------------------ + --------------------------- + ----------------------
6 72 72 72 72
$$- \frac{5 \sqrt{6} \log{\left(\frac{\sqrt{6}}{2} \right)}}{72} + \frac{5 \sqrt{6} \log{\left(1 + \frac{\sqrt{6}}{2} \right)}}{72} + \frac{7}{6} - \frac{5 \sqrt{6} \left(\log{\left(-1 + \frac{\sqrt{6}}{2} \right)} + i \pi\right)}{72} + \frac{5 \sqrt{6} \left(\log{\left(\frac{\sqrt{6}}{2} \right)} + i \pi\right)}{72}$$
=
=
/ / ___\\ / ___\ / / ___\\ / ___\
___ | | \/ 6 || ___ |\/ 6 | ___ | |\/ 6 || ___ | \/ 6 |
5*\/ 6 *|pi*I + log|-1 + -----|| 5*\/ 6 *log|-----| 5*\/ 6 *|pi*I + log|-----|| 5*\/ 6 *log|1 + -----|
7 \ \ 2 // \ 2 / \ \ 2 // \ 2 /
- - -------------------------------- - ------------------ + --------------------------- + ----------------------
6 72 72 72 72
$$- \frac{5 \sqrt{6} \log{\left(\frac{\sqrt{6}}{2} \right)}}{72} + \frac{5 \sqrt{6} \log{\left(1 + \frac{\sqrt{6}}{2} \right)}}{72} + \frac{7}{6} - \frac{5 \sqrt{6} \left(\log{\left(-1 + \frac{\sqrt{6}}{2} \right)} + i \pi\right)}{72} + \frac{5 \sqrt{6} \left(\log{\left(\frac{\sqrt{6}}{2} \right)} + i \pi\right)}{72}$$
7/6 - 5*sqrt(6)*(pi*i + log(-1 + sqrt(6)/2))/72 - 5*sqrt(6)*log(sqrt(6)/2)/72 + 5*sqrt(6)*(pi*i + log(sqrt(6)/2))/72 + 5*sqrt(6)*log(1 + sqrt(6)/2)/72
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.