Mister Exam

Integral of log(x-1) 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 - 1) dx
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$$\int\limits_{0}^{1} \log{\left(x - 1 \right)}\, dx$$
Integral(log(x - 1), (x, 0, 1))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    1. Let .

      Then let and substitute :

      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:

      Now substitute back in:

    Method #2

    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. Rewrite the integrand:

    3. Integrate term-by-term:

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

      1. Let .

        Then let and substitute :

        1. The integral of is .

        Now substitute back in:

      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 - 1) dx = 1 + C - x + (x - 1)*log(x - 1)
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$$\int \log{\left(x - 1 \right)}\, dx = C - x + \left(x - 1\right) \log{\left(x - 1 \right)} + 1$$
The graph
The answer [src]
-1 + pi*I
$$-1 + i \pi$$
=
=
-1 + pi*I
$$-1 + i \pi$$
-1 + pi*i
Numerical answer [src]
(-1.0 + 3.14159265358979j)
(-1.0 + 3.14159265358979j)
The graph
Integral of log(x-1) dx

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