Sr Examen
Integral de 1/(2+sqrt^3(x-5)) dx
Solución
Ha introducido
[src]
9 / | | 1 | -------------- dx | 3 | _______ | 2 + \/ x - 5 | / 6
$$\int\limits_{6}^{9} \frac{1}{\left(\sqrt{x - 5}\right)^{3} + 2}\, dx$$
Integral(1/(2 + (sqrt(x - 5))^3), (x, 6, 9))
Respuesta (Indefinida)
[src]
/ pi*I\ / 5*pi*I\
-2*pi*I | ----| 2*pi*I | ------|
/ 2/3 ________ pi*I\ ------- | 2/3 ________ 3 | ------ | 2/3 ________ 3 |
/ 2/3 | 2 *\/ -5 + x *e | 2/3 3 | 2 *\/ -5 + x *e | 2/3 3 | 2 *\/ -5 + x *e |
| 2*2 *Gamma(2/3)*log|1 - ---------------------| 2*2 *e *Gamma(2/3)*log|1 - ---------------------| 2*2 *e *Gamma(2/3)*log|1 - -----------------------|
| 1 \ 2 / \ 2 / \ 2 /
| -------------- dx = C - ------------------------------------------------ - --------------------------------------------------------- - ----------------------------------------------------------
| 3 9*Gamma(5/3) 9*Gamma(5/3) 9*Gamma(5/3)
| _______
| 2 + \/ x - 5
|
/
$$\int \frac{1}{\left(\sqrt{x - 5}\right)^{3} + 2}\, dx = C - \frac{2 \cdot 2^{\frac{2}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(- \frac{2^{\frac{2}{3}} \sqrt{x - 5} e^{\frac{i \pi}{3}}}{2} + 1 \right)} \Gamma\left(\frac{2}{3}\right)}{9 \Gamma\left(\frac{5}{3}\right)} - \frac{2 \cdot 2^{\frac{2}{3}} \log{\left(- \frac{2^{\frac{2}{3}} \sqrt{x - 5} e^{i \pi}}{2} + 1 \right)} \Gamma\left(\frac{2}{3}\right)}{9 \Gamma\left(\frac{5}{3}\right)} - \frac{2 \cdot 2^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \log{\left(- \frac{2^{\frac{2}{3}} \sqrt{x - 5} e^{\frac{5 i \pi}{3}}}{2} + 1 \right)} \Gamma\left(\frac{2}{3}\right)}{9 \Gamma\left(\frac{5}{3}\right)}$$
Gráfica
Respuesta
[src]
/ ___ 2/3 ___\ / ___ 2/3 ___\
2/3 ___ |\/ 3 2*2 *\/ 3 | 2/3 ___ |\/ 3 2 *\/ 3 |
2/3 / 3 ___\ 2/3 / 3 ___ 2/3\ 2/3 / 3 ___\ 2/3 / 3 ___ 2/3\ 2 *\/ 3 *atan|----- - ------------| 2 *\/ 3 *atan|----- - ----------|
2 *log\2 + \/ 2 / 2 *log\4 - 4*\/ 2 + 4*2 / 2 *log\1 + \/ 2 / 2 *log\16 - 8*\/ 2 + 4*2 / \ 3 3 / \ 3 3 /
- ------------------- - ------------------------------ + ------------------- + ------------------------------- - ------------------------------------- + -----------------------------------
3 6 3 6 3 3
$$- \frac{2^{\frac{2}{3}} \log{\left(\sqrt[3]{2} + 2 \right)}}{3} - \frac{2^{\frac{2}{3}} \log{\left(- 4 \sqrt[3]{2} + 4 + 4 \cdot 2^{\frac{2}{3}} \right)}}{6} + \frac{2^{\frac{2}{3}} \sqrt{3} \operatorname{atan}{\left(- \frac{2^{\frac{2}{3}} \sqrt{3}}{3} + \frac{\sqrt{3}}{3} \right)}}{3} + \frac{2^{\frac{2}{3}} \log{\left(1 + \sqrt[3]{2} \right)}}{3} + \frac{2^{\frac{2}{3}} \log{\left(- 8 \sqrt[3]{2} + 4 \cdot 2^{\frac{2}{3}} + 16 \right)}}{6} - \frac{2^{\frac{2}{3}} \sqrt{3} \operatorname{atan}{\left(- \frac{2 \cdot 2^{\frac{2}{3}} \sqrt{3}}{3} + \frac{\sqrt{3}}{3} \right)}}{3}$$
=
=
/ ___ 2/3 ___\ / ___ 2/3 ___\
2/3 ___ |\/ 3 2*2 *\/ 3 | 2/3 ___ |\/ 3 2 *\/ 3 |
2/3 / 3 ___\ 2/3 / 3 ___ 2/3\ 2/3 / 3 ___\ 2/3 / 3 ___ 2/3\ 2 *\/ 3 *atan|----- - ------------| 2 *\/ 3 *atan|----- - ----------|
2 *log\2 + \/ 2 / 2 *log\4 - 4*\/ 2 + 4*2 / 2 *log\1 + \/ 2 / 2 *log\16 - 8*\/ 2 + 4*2 / \ 3 3 / \ 3 3 /
- ------------------- - ------------------------------ + ------------------- + ------------------------------- - ------------------------------------- + -----------------------------------
3 6 3 6 3 3
$$- \frac{2^{\frac{2}{3}} \log{\left(\sqrt[3]{2} + 2 \right)}}{3} - \frac{2^{\frac{2}{3}} \log{\left(- 4 \sqrt[3]{2} + 4 + 4 \cdot 2^{\frac{2}{3}} \right)}}{6} + \frac{2^{\frac{2}{3}} \sqrt{3} \operatorname{atan}{\left(- \frac{2^{\frac{2}{3}} \sqrt{3}}{3} + \frac{\sqrt{3}}{3} \right)}}{3} + \frac{2^{\frac{2}{3}} \log{\left(1 + \sqrt[3]{2} \right)}}{3} + \frac{2^{\frac{2}{3}} \log{\left(- 8 \sqrt[3]{2} + 4 \cdot 2^{\frac{2}{3}} + 16 \right)}}{6} - \frac{2^{\frac{2}{3}} \sqrt{3} \operatorname{atan}{\left(- \frac{2 \cdot 2^{\frac{2}{3}} \sqrt{3}}{3} + \frac{\sqrt{3}}{3} \right)}}{3}$$
-2^(2/3)*log(2 + 2^(1/3))/3 - 2^(2/3)*log(4 - 4*2^(1/3) + 4*2^(2/3))/6 + 2^(2/3)*log(1 + 2^(1/3))/3 + 2^(2/3)*log(16 - 8*2^(1/3) + 4*2^(2/3))/6 - 2^(2/3)*sqrt(3)*atan(sqrt(3)/3 - 2*2^(2/3)*sqrt(3)/3)/3 + 2^(2/3)*sqrt(3)*atan(sqrt(3)/3 - 2^(2/3)*sqrt(3)/3)/3
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.