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

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                    
  /                    
 |                     
 |          1          
 |  1*-------------- dx
 |       2             
 |    2*x  + 3*x + 1   
 |                     
/                      
0                      
$$\int\limits_{0}^{1} 1 \cdot \frac{1}{2 x^{2} + 3 x + 1}\, dx$$
Integral(1/(2*x^2 + 3*x + 1), (x, 0, 1))
Detail solution
  1. Rewrite the integrand:

  2. Integrate term-by-term:

    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 a constant times a function is the constant times the integral of the function:

          1. The integral of is .

          So, the result is:

        Now substitute back in:

      So, 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:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                   
 |                                                    
 |         1                                          
 | 1*-------------- dx = C - log(1 + x) + log(1 + 2*x)
 |      2                                             
 |   2*x  + 3*x + 1                                   
 |                                                    
/                                                     
$$\log \left(2\,x+1\right)-\log \left(x+1\right)$$
The graph
The answer [src]
log(3/2)
$$\log 3-\log 2$$
=
=
log(3/2)
$$\log{\left(\frac{3}{2} \right)}$$
Numerical answer [src]
0.405465108108164
0.405465108108164
The graph
Integral of 1/(2x^2+3x+1) dx

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