Integral de 1/(2+sqrt^3(x-5)) dx
Solución
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
|
/
∫(x−5)3+21dx=C−9Γ(35)2⋅232e−32iπlog(−2232x−5e3iπ+1)Γ(32)−9Γ(35)2⋅232log(−2232x−5eiπ+1)Γ(32)−9Γ(35)2⋅232e32iπlog(−2232x−5e35iπ+1)Γ(32)
Gráfica
/ ___ 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
−3232log(32+2)−6232log(−432+4+4⋅232)+32323atan(−32323+33)+3232log(1+32)+6232log(−832+4⋅232+16)−32323atan(−32⋅2323+33)
=
/ ___ 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
−3232log(32+2)−6232log(−432+4+4⋅232)+32323atan(−32323+33)+3232log(1+32)+6232log(−832+4⋅232+16)−32323atan(−32⋅2323+33)
-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.