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2x-3/(x-1)(x+2)

Integral of 2x-3/(x-1)(x+2) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                         
  /                         
 |                          
 |  /        3          \   
 |  |2*x - -----*(x + 2)| dx
 |  \      x - 1        /   
 |                          
/                           
0                           
$$\int\limits_{0}^{1} \left(2 x - \frac{3}{x - 1} \left(x + 2\right)\right)\, dx$$
Integral(2*x - 3/(x - 1)*(x + 2), (x, 0, 1))
Detail solution
  1. Integrate term-by-term:

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. The integral of is when :

      So, the result is:

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. The integral of a constant times a function is the constant times the integral of the function:

        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. Let .

                Then let and substitute :

                1. The integral of is .

                Now substitute back in:

              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:

        So, the result is:

      So, the result is:

    The result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                       
 |                                                        
 | /        3          \           2                      
 | |2*x - -----*(x + 2)| dx = C + x  - 9*log(-1 + x) - 3*x
 | \      x - 1        /                                  
 |                                                        
/                                                         
$$\int \left(2 x - \frac{3}{x - 1} \left(x + 2\right)\right)\, dx = C + x^{2} - 3 x - 9 \log{\left(x - 1 \right)}$$
The graph
The answer [src]
oo + 9*pi*I
$$\infty + 9 i \pi$$
=
=
oo + 9*pi*I
$$\infty + 9 i \pi$$
oo + 9*pi*i
Numerical answer [src]
394.818611075975
394.818611075975
The graph
Integral of 2x-3/(x-1)(x+2) dx

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