Integral of lnx-1 dx

The solution

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 |  (log(x) - 1) dx
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$$\int\limits_{0}^{1} \left(\log{\left(x \right)} - 1\right)\, dx$$

Integral(log(x) - 1, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. Use integration by parts:
  
  $\int \operatorname{u} \operatorname{dv} = \operatorname{u}\operatorname{v} - \int \operatorname{v} \operatorname{du}$
  
  Let $u{\left(x \right)} = \log{\left(x \right)}$ and let $\operatorname{dv}{\left(x \right)} = 1$ .
  
  Then $\operatorname{du}{\left(x \right)} = \frac{1}{x}$ .
  
  To find $v{\left(x \right)}$ :
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int 1\, dx = x$
  Now evaluate the sub-integral.
2. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, dx = x$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-1\right)\, dx = - x$
The result is: $x \log{\left(x \right)} - 2 x$
Now simplify:

$x \left(\log{\left(x \right)} - 2\right)$
Add the constant of integration:

$x \left(\log{\left(x \right)} - 2\right)+ \mathrm{constant}$

The answer is:

$x \left(\log{\left(x \right)} - 2\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

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 | (log(x) - 1) dx = C - 2*x + x*log(x)
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$$\int \left(\log{\left(x \right)} - 1\right)\, dx = C + x \log{\left(x \right)} - 2 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-2

$$-2$$

-2

$$-2$$

-2

Numerical answer [src]

-2.0

-2.0

The graph

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

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Identical expressions

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Integral of lnx-1 dx

Limits of integration:

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Piecewise:

The solution