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Integral of 1/x+y+z+1 dx

The solution

You have entered [src]

  1                   
  /                   
 |                    
 |  /1            \   
 |  |- + y + z + 1| dx
 |  \x            /   
 |                    
/                     
0

$$\int\limits_{0}^{1} \left(\left(z + \left(y + \frac{1}{x}\right)\right) + 1\right)\, dx$$

Integral(1/x + y + z + 1, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. Integrate term-by-term:
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int z\, dx = x z$
  1. Integrate term-by-term:
    1. The integral of a constant is the constant times the variable of integration:
      
      $\int y\, dx = x y$
    1. The integral of $\frac{1}{x}$ is $\log{\left(x \right)}$ .
    The result is: $x y + \log{\left(x \right)}$
  The result is: $x y + x z + \log{\left(x \right)}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, dx = x$
The result is: $x y + x z + x + \log{\left(x \right)}$
Add the constant of integration:

$x y + x z + x + \log{\left(x \right)}+ \mathrm{constant}$

The answer is:

$x y + x z + x + \log{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                               
 |                                                
 | /1            \                                
 | |- + y + z + 1| dx = C + x + x*y + x*z + log(x)
 | \x            /                                
 |                                                
/

$$\int \left(\left(z + \left(y + \frac{1}{x}\right)\right) + 1\right)\, dx = C + x y + x z + x + \log{\left(x \right)}$$

Simplify

The answer [src]

oo + y + z

$$y + z + \infty$$

oo + y + z

$$y + z + \infty$$

oo + y + z

Use the examples entering the upper and lower limits of integration.

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Integral of 1/x+y+z+1 dx

Limits of integration:

The graph:

Piecewise:

The solution