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Resolución de integrales/ (x+2)/ (√x+1)/ (6*√x+2)/((x+2)^2*(√x+1))

Integral de (6*√x+2)/((x+2)^2*(√x+1)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 -7/8                       
   /                        
  |                         
  |          ___            
  |      6*\/ x  + 2        
  |  -------------------- dx
  |         2 /  ___    \   
  |  (x + 2) *\\/ x  + 1/   
  |                         
 /                          
-14                         
----                        
 15
$$\int\limits_{- \frac{14}{15}}^{- \frac{7}{8}} \frac{6 \sqrt{x} + 2}{\left(\sqrt{x} + 1\right) \left(x + 2\right)^{2}}\, dx$$ 
Integral((6*sqrt(x) + 2)/(((x + 2)^2*(sqrt(x) + 1))), (x, -14/15, -7/8))
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
           /        _____\                                 /        ____\                                           /  ___\                  /  _____\
           |    I*\/ 210 |                     /16\        |    I*\/ 14 |                                  ___      |\/ 7 |         ___      |\/ 105 |
      8*log|1 + ---------|                4*log|--|   8*log|1 + --------|         ____       _____   2*I*\/ 2 *atanh|-----|   2*I*\/ 2 *atanh|-------|
 49        \        15   /   4*log(9/8)        \15/        \       4    /   8*I*\/ 14    I*\/ 210                   \  4  /                  \   15  /
--- - -------------------- - ---------- + --------- + ------------------- - ---------- + --------- - ---------------------- + ------------------------
216            9                 9            9                9                27           12                9                         9
$$- \frac{4 \log{\left(\frac{9}{8} \right)}}{9} + \frac{4 \log{\left(\frac{16}{15} \right)}}{9} + \frac{49}{216} - \frac{8 \sqrt{14} i}{27} - \frac{8 \log{\left(1 + \frac{\sqrt{210} i}{15} \right)}}{9} - \frac{2 \sqrt{2} i \operatorname{atanh}{\left(\frac{\sqrt{7}}{4} \right)}}{9} + \frac{2 \sqrt{2} i \operatorname{atanh}{\left(\frac{\sqrt{105}}{15} \right)}}{9} + \frac{8 \log{\left(1 + \frac{\sqrt{14} i}{4} \right)}}{9} + \frac{\sqrt{210} i}{12}$$ 
=
= 
           /        _____\                                 /        ____\                                           /  ___\                  /  _____\
           |    I*\/ 210 |                     /16\        |    I*\/ 14 |                                  ___      |\/ 7 |         ___      |\/ 105 |
      8*log|1 + ---------|                4*log|--|   8*log|1 + --------|         ____       _____   2*I*\/ 2 *atanh|-----|   2*I*\/ 2 *atanh|-------|
 49        \        15   /   4*log(9/8)        \15/        \       4    /   8*I*\/ 14    I*\/ 210                   \  4  /                  \   15  /
--- - -------------------- - ---------- + --------- + ------------------- - ---------- + --------- - ---------------------- + ------------------------
216            9                 9            9                9                27           12                9                         9
$$- \frac{4 \log{\left(\frac{9}{8} \right)}}{9} + \frac{4 \log{\left(\frac{16}{15} \right)}}{9} + \frac{49}{216} - \frac{8 \sqrt{14} i}{27} - \frac{8 \log{\left(1 + \frac{\sqrt{210} i}{15} \right)}}{9} - \frac{2 \sqrt{2} i \operatorname{atanh}{\left(\frac{\sqrt{7}}{4} \right)}}{9} + \frac{2 \sqrt{2} i \operatorname{atanh}{\left(\frac{\sqrt{105}}{15} \right)}}{9} + \frac{8 \log{\left(1 + \frac{\sqrt{14} i}{4} \right)}}{9} + \frac{\sqrt{210} i}{12}$$ 
49/216 - 8*log(1 + i*sqrt(210)/15)/9 - 4*log(9/8)/9 + 4*log(16/15)/9 + 8*log(1 + i*sqrt(14)/4)/9 - 8*i*sqrt(14)/27 + i*sqrt(210)/12 - 2*i*sqrt(2)*atanh(sqrt(7)/4)/9 + 2*i*sqrt(2)*atanh(sqrt(105)/15)/9
Respuesta numérica [src] 
(0.189571192304873 + 0.0970958016623237j)
(0.189571192304873 + 0.0970958016623237j)

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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