Sr Examen
Integral de 1dx/(x^2sqrt2x-4) dx
Solución
Ha introducido
[src]
1 / | | 1 | -------------- dx | 2 _____ | x *\/ 2*x - 4 | / 0
$$\int\limits_{0}^{1} \frac{1}{x^{2} \sqrt{2 x} - 4}\, dx$$
Integral(1/(x^2*sqrt(2*x) - 4), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ 2*pi*I\ / 6*pi*I\ / 4*pi*I\ / 8*pi*I\
-4*pi*I | ------| -2*pi*I | ------| 2*pi*I | ------| 4*pi*I | ------|
/ 7/10 ___\ ------- | 7/10 ___ 5 | ------- | 7/10 ___ 5 | ------ | 7/10 ___ 5 | ------ | 7/10 ___ 5 |
/ 3/5 | 2 *\/ x | 3/5 5 | 2 *\/ x *e | 3/5 5 | 2 *\/ x *e | 3/5 5 | 2 *\/ x *e | 3/5 5 | 2 *\/ x *e |
| 2 *Gamma(2/5)*log|1 - -----------| 2 *e *Gamma(2/5)*log|1 - -------------------| 2 *e *Gamma(2/5)*log|1 - -------------------| 2 *e *Gamma(2/5)*log|1 - -------------------| 2 *e *Gamma(2/5)*log|1 - -------------------|
| 1 \ 2 / \ 2 / \ 2 / \ 2 / \ 2 /
| -------------- dx = C + ------------------------------------ + ----------------------------------------------------- + ----------------------------------------------------- + ---------------------------------------------------- + ----------------------------------------------------
| 2 _____ 25*Gamma(7/5) 25*Gamma(7/5) 25*Gamma(7/5) 25*Gamma(7/5) 25*Gamma(7/5)
| x *\/ 2*x - 4
|
/
$$\int \frac{1}{x^{2} \sqrt{2 x} - 4}\, dx = C + \frac{2^{\frac{3}{5}} \log{\left(- \frac{2^{\frac{7}{10}} \sqrt{x}}{2} + 1 \right)} \Gamma\left(\frac{2}{5}\right)}{25 \Gamma\left(\frac{7}{5}\right)} + \frac{2^{\frac{3}{5}} e^{- \frac{4 i \pi}{5}} \log{\left(- \frac{2^{\frac{7}{10}} \sqrt{x} e^{\frac{2 i \pi}{5}}}{2} + 1 \right)} \Gamma\left(\frac{2}{5}\right)}{25 \Gamma\left(\frac{7}{5}\right)} + \frac{2^{\frac{3}{5}} e^{\frac{2 i \pi}{5}} \log{\left(- \frac{2^{\frac{7}{10}} \sqrt{x} e^{\frac{4 i \pi}{5}}}{2} + 1 \right)} \Gamma\left(\frac{2}{5}\right)}{25 \Gamma\left(\frac{7}{5}\right)} + \frac{2^{\frac{3}{5}} e^{- \frac{2 i \pi}{5}} \log{\left(- \frac{2^{\frac{7}{10}} \sqrt{x} e^{\frac{6 i \pi}{5}}}{2} + 1 \right)} \Gamma\left(\frac{2}{5}\right)}{25 \Gamma\left(\frac{7}{5}\right)} + \frac{2^{\frac{3}{5}} e^{\frac{4 i \pi}{5}} \log{\left(- \frac{2^{\frac{7}{10}} \sqrt{x} e^{\frac{8 i \pi}{5}}}{2} + 1 \right)} \Gamma\left(\frac{2}{5}\right)}{25 \Gamma\left(\frac{7}{5}\right)}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.