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Solving integrals/ 1/x+y+z+1

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

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
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∫01((z+(y+1x))+1) dx\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

  1. Integrate term-by-term:

    1. Integrate term-by-term:

      1. The integral of a constant is the constant times the variable of integration:

        ∫z dx=xz\int z\, dx = x z

      1. Integrate term-by-term:

        1. The integral of a constant is the constant times the variable of integration:

          ∫y dx=xy\int y\, dx = x y

        1. The integral of 1x\frac{1}{x} is log⁡(x)\log{\left(x \right)}.

        The result is: xy+log⁡(x)x y + \log{\left(x \right)}

      The result is: xy+xz+log⁡(x)x y + x z + \log{\left(x \right)}

    1. The integral of a constant is the constant times the variable of integration:

      ∫1 dx=x\int 1\, dx = x

    The result is: xy+xz+x+log⁡(x)x y + x z + x + \log{\left(x \right)}

  2. Add the constant of integration:

    xy+xz+x+log⁡(x)+constantx y + x z + x + \log{\left(x \right)}+ \mathrm{constant}

The answer is:

xy+xz+x+log⁡(x)+constantx y + x z + x + \log{\left(x \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫((z+(y+1x))+1) dx=C+xy+xz+x+log⁡(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+∞y + z + \infty 
=
= 
oo + y + z
y+z+∞y + z + \infty 
oo + y + z

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

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