Mister Exam

Integral of log2x dx

Limits of integration:

from to

The graph:

from to

Enter:

The solution

You have entered [src]
  1            
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 |  log(2*x) dx
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$$\int\limits_{0}^{1} \log{\left(2 x \right)}\, dx$$
Integral(log(2*x), (x, 0, 1))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    1. Let .

      Then let and substitute :

      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:

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

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                
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 | log(2*x) dx = C - x + x*log(2*x)
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$$\int \log{\left(2 x \right)}\, dx = C + x \log{\left(2 x \right)} - x$$
The graph
The answer [src]
-1 + log(2)
$$-1 + \log{\left(2 \right)}$$
=
=
-1 + log(2)
$$-1 + \log{\left(2 \right)}$$
-1 + log(2)
Numerical answer [src]
-0.306852819440055
-0.306852819440055
The graph
Integral of log2x dx

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

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