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Integral of d{x}:
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Integral of x^3*ln(x)
Integral of x*ln(x+1)dx
Graphing y =:
1/(x^2+5x+6)
Identical expressions
one /(x^ two +5x+ six)
1 divide by (x squared plus 5x plus 6)
one divide by (x to the power of two plus 5x plus six)
1/(x2+5x+6)
1/x2+5x+6
1/(x²+5x+6)
1/(x to the power of 2+5x+6)
1/x^2+5x+6
1 divide by (x^2+5x+6)
1/(x^2+5x+6)dx
Similar expressions
1/(x^2-5x+6)
1/(x^2+5x-6)

Solving integrals/ 1/(x^2+5x+6)

Integral of 1/(x^2+5x+6) dx

The solution

You have entered [src]

  1                  
  /                  
 |                   
 |         1         
 |  1*------------ dx
 |     2             
 |    x  + 5*x + 6   
 |                   
/                    
0

$$\int\limits_{0}^{1} 1 \cdot \frac{1}{x^{2} + 5 x + 6}\, dx$$

Integral(1/(x^2 + 5*x + 6), (x, 0, 1))

Detail solution

Rewrite the integrand:

$1 \cdot \frac{1}{x^{2} + 5 x + 6} = - \frac{1}{x + 3} + \frac{1}{x + 2}$
Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{1}{x + 3}\right)\, dx = - \int \frac{1}{x + 3}\, dx$
  1. Let $u = x + 3$ .
    
    Then let $du = dx$ and substitute $du$ :
    
    $\int \frac{1}{u}\, du$
    1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
    Now substitute $u$ back in:
    
    $\log{\left(x + 3 \right)}$
  So, the result is: $- \log{\left(x + 3 \right)}$
1. Let $u = x + 2$ .
  
  Then let $du = dx$ and substitute $du$ :
  
  $\int \frac{1}{u}\, du$
  1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
  Now substitute $u$ back in:
  
  $\log{\left(x + 2 \right)}$
The result is: $\log{\left(x + 2 \right)} - \log{\left(x + 3 \right)}$
Add the constant of integration:

$\log{\left(x + 2 \right)} - \log{\left(x + 3 \right)}+ \mathrm{constant}$

The answer is:

$\log{\left(x + 2 \right)} - \log{\left(x + 3 \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                               
 |                                                
 |        1                                       
 | 1*------------ dx = C - log(3 + x) + log(2 + x)
 |    2                                           
 |   x  + 5*x + 6                                 
 |                                                
/

$$\log \left(x+2\right)-\log \left(x+3\right)$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-log(2) - log(4) + 2*log(3)

$$-\log 4+2\,\log 3-\log 2$$

-log(2) - log(4) + 2*log(3)

$$- \log{\left(4 \right)} - \log{\left(2 \right)} + 2 \log{\left(3 \right)}$$

Упростить

Numerical answer [src]

0.117783035656383

0.117783035656383

The graph

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

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Identical expressions

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Integral of 1/(x^2+5x+6) dx

Limits of integration:

The graph:

Piecewise:

The solution