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Resolución de integrales/ (x+1)/ sqrt(x)/ (dx)/(3+sqrt(x)/(x+1))

Integral de (dx)/(3+sqrt(x)/(x+1)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 24             
  /             
 |              
 |      1       
 |  --------- dx
 |        ___   
 |      \/ x    
 |  3 + -----   
 |      x + 1   
 |              
/               
15
$$\int\limits_{15}^{24} \frac{1}{\frac{\sqrt{x}}{x + 1} + 3}\, dx$$ 
Integral(1/(3 + sqrt(x)/(x + 1)), (x, 15, 24))
Respuesta (Indefinida) [src] 
                                                                         /    ____ /1     ___\\
                                                                         |6*\/ 35 *|- + \/ x ||
  /                                                             ____     |         \6        /|
 |                        ___          /      ___      \   34*\/ 35 *atan|--------------------|
 |     1              2*\/ x    x   log\3 + \/ x  + 3*x/                 \         35         /
 | --------- dx = C - ------- + - + -------------------- + ------------------------------------
 |       ___             9      3            27                            945                 
 |     \/ x                                                                                    
 | 3 + -----                                                                                   
 |     x + 1                                                                                   
 |                                                                                             
/
$$\int \frac{1}{\frac{\sqrt{x}}{x + 1} + 3}\, dx = C - \frac{2 \sqrt{x}}{9} + \frac{x}{3} + \frac{\log{\left(\sqrt{x} + 3 x + 3 \right)}}{27} + \frac{34 \sqrt{35} \operatorname{atan}{\left(\frac{6 \sqrt{35} \left(\sqrt{x} + \frac{1}{6}\right)}{35} \right)}}{945}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
                                                                                    /  ____       ____\                 /  ____        _____\
                                                                           ____     |\/ 35    6*\/ 21 |        ____     |\/ 35    12*\/ 210 |
        ___      /           ____\      /           ___\       ____   34*\/ 35 *atan|------ + --------|   34*\/ 35 *atan|------ + ----------|
    4*\/ 6    log\576 + 12*\/ 15 /   log\900 + 24*\/ 6 /   2*\/ 15                  \  35        7    /                 \  35         35    /
3 - ------- - -------------------- + ------------------- + -------- - --------------------------------- + -----------------------------------
       9               27                     27              9                      945                                  945
$$- \frac{4 \sqrt{6}}{9} - \frac{34 \sqrt{35} \operatorname{atan}{\left(\frac{\sqrt{35}}{35} + \frac{6 \sqrt{21}}{7} \right)}}{945} - \frac{\log{\left(12 \sqrt{15} + 576 \right)}}{27} + \frac{\log{\left(24 \sqrt{6} + 900 \right)}}{27} + \frac{34 \sqrt{35} \operatorname{atan}{\left(\frac{\sqrt{35}}{35} + \frac{12 \sqrt{210}}{35} \right)}}{945} + \frac{2 \sqrt{15}}{9} + 3$$ 
=
= 
                                                                                    /  ____       ____\                 /  ____        _____\
                                                                           ____     |\/ 35    6*\/ 21 |        ____     |\/ 35    12*\/ 210 |
        ___      /           ____\      /           ___\       ____   34*\/ 35 *atan|------ + --------|   34*\/ 35 *atan|------ + ----------|
    4*\/ 6    log\576 + 12*\/ 15 /   log\900 + 24*\/ 6 /   2*\/ 15                  \  35        7    /                 \  35         35    /
3 - ------- - -------------------- + ------------------- + -------- - --------------------------------- + -----------------------------------
       9               27                     27              9                      945                                  945
$$- \frac{4 \sqrt{6}}{9} - \frac{34 \sqrt{35} \operatorname{atan}{\left(\frac{\sqrt{35}}{35} + \frac{6 \sqrt{21}}{7} \right)}}{945} - \frac{\log{\left(12 \sqrt{15} + 576 \right)}}{27} + \frac{\log{\left(24 \sqrt{6} + 900 \right)}}{27} + \frac{34 \sqrt{35} \operatorname{atan}{\left(\frac{\sqrt{35}}{35} + \frac{12 \sqrt{210}}{35} \right)}}{945} + \frac{2 \sqrt{15}}{9} + 3$$ 
3 - 4*sqrt(6)/9 - log(576 + 12*sqrt(15))/27 + log(900 + 24*sqrt(6))/27 + 2*sqrt(15)/9 - 34*sqrt(35)*atan(sqrt(35)/35 + 6*sqrt(21)/7)/945 + 34*sqrt(35)*atan(sqrt(35)/35 + 12*sqrt(210)/35)/945
Respuesta numérica [src] 
2.79803764066357
2.79803764066357

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

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