Mister Exam

Other calculators


(x+3)/(x-4)

Integral of (x+3)/(x-4) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1         
  /         
 |          
 |  x + 3   
 |  ----- dx
 |  x - 4   
 |          
/           
0           
$$\int\limits_{0}^{1} \frac{x + 3}{x - 4}\, dx$$
Integral((x + 3)/(x - 4), (x, 0, 1))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    1. Rewrite the integrand:

    2. 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:

    Method #2

    1. Rewrite the integrand:

    2. Integrate term-by-term:

      1. Rewrite the integrand:

      2. 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:

      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. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                
 |                                 
 | x + 3                           
 | ----- dx = C + x + 7*log(-4 + x)
 | x - 4                           
 |                                 
/                                  
$$\int \frac{x + 3}{x - 4}\, dx = C + x + 7 \log{\left(x - 4 \right)}$$
The graph
The answer [src]
1 - 7*log(4) + 7*log(3)
$$- 7 \log{\left(4 \right)} + 1 + 7 \log{\left(3 \right)}$$
=
=
1 - 7*log(4) + 7*log(3)
$$- 7 \log{\left(4 \right)} + 1 + 7 \log{\left(3 \right)}$$
1 - 7*log(4) + 7*log(3)
Numerical answer [src]
-1.01377450716247
-1.01377450716247
The graph
Integral of (x+3)/(x-4) dx

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