Mister Exam

Integral of -lnx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1           
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 |  -log(x) dx
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$$\int\limits_{0}^{1} \left(- \log{\left(x \right)}\right)\, dx$$
Integral(-log(x), (x, 0, 1))
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

    1. Use integration by parts:

      Let and let .

      Then .

      To find :

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

      Now evaluate the sub-integral.

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

    So, the result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                             
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 | -log(x) dx = C + x - x*log(x)
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$$\int \left(- \log{\left(x \right)}\right)\, dx = C - x \log{\left(x \right)} + x$$
The graph
The answer [src]
1
$$1$$
=
=
1
$$1$$
1
Numerical answer [src]
1.0
1.0
The graph
Integral of -lnx dx

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