Mister Exam

Other calculators


ln(x+1)

Integral of ln(x+1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

        1. Let .

          Then let and substitute :

          1. The integral of is .

          Now substitute back in:

        So, the result is:

      The result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                               
 |                                                
 | log(x + 1) dx = -1 + C - x + (x + 1)*log(x + 1)
 |                                                
/                                                 
$$\int \log{\left(x + 1 \right)}\, dx = C - x + \left(x + 1\right) \log{\left(x + 1 \right)} - 1$$
The graph
The answer [src]
-1 + 2*log(2)
$$-1 + 2 \log{\left(2 \right)}$$
=
=
-1 + 2*log(2)
$$-1 + 2 \log{\left(2 \right)}$$
Numerical answer [src]
0.386294361119891
0.386294361119891
The graph
Integral of ln(x+1) dx

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