Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of 1/(x^2+9x+20)
Integral of sin(4x)cos(4x)dx
Integral of 9dx
Integral of cos^2t*sint
Identical expressions
one /(x^ two +9x+ twenty)
1 divide by (x squared plus 9x plus 20)
one divide by (x to the power of two plus 9x plus twenty)
1/(x2+9x+20)
1/x2+9x+20
1/(x²+9x+20)
1/(x to the power of 2+9x+20)
1/x^2+9x+20
1 divide by (x^2+9x+20)
1/(x^2+9x+20)dx
Similar expressions
1/(x^2+9x-20)
1/(x^2-9x+20)

Solving integrals/ 1/(x^2+9x+20)

Integral of 1/(x^2+9x+20) dx

The solution

You have entered [src]

 oo                   
  /                   
 |                    
 |          1         
 |  1*------------- dx
 |     2              
 |    x  + 9*x + 20   
 |                    
/                     
7

$$\int\limits_{7}^{\infty} 1 \cdot \frac{1}{x^{2} + 9 x + 20}\, dx$$

Simplify

Detail solution

Rewrite the integrand:

$1 \cdot \frac{1}{x^{2} + 9 x + 20} = - \frac{1}{x + 5} + \frac{1}{x + 4}$
Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{1}{x + 5}\right)\, dx = - \int \frac{1}{x + 5}\, dx$
  1. Let $u = x + 5$ .
    
    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:
    
    $\log{\left(x + 5 \right)}$
  So, the result is: $- \log{\left(x + 5 \right)}$
1. Let $u = x + 4$ .
  
  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:
  
  $\log{\left(x + 4 \right)}$
The result is: $\log{\left(x + 4 \right)} - \log{\left(x + 5 \right)}$
Add the constant of integration:

$\log{\left(x + 4 \right)} - \log{\left(x + 5 \right)}+ \mathrm{constant}$

The answer is:

$\log{\left(x + 4 \right)} - \log{\left(x + 5 \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                
 |                                                 
 |         1                                       
 | 1*------------- dx = C - log(5 + x) + log(4 + x)
 |    2                                            
 |   x  + 9*x + 20                                 
 |                                                 
/

$$\log \left(x+4\right)-\log \left(x+5\right)$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-log(11) + log(12)

$$- \log{\left(11 \right)} + \log{\left(12 \right)}$$

-log(11) + log(12)

$$- \log{\left(11 \right)} + \log{\left(12 \right)}$$

Simplify

The graph

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of 1/(x^2+9x+20) dx

Limits of integration:

The graph:

Piecewise:

The solution