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Integral of d{x}:
Integral of sin²xcos²x
Integral of sin^n(x)
Integral of dx/(x^2+4*x+5)
Integral of e^(-x)/sqrt(x)
Identical expressions
dx/(x^ two + four *x+ five)
dx divide by (x squared plus 4 multiply by x plus 5)
dx divide by (x to the power of two plus four multiply by x plus five)
dx/(x2+4*x+5)
dx/x2+4*x+5
dx/(x²+4*x+5)
dx/(x to the power of 2+4*x+5)
dx/(x^2+4x+5)
dx/(x2+4x+5)
dx/x2+4x+5
dx/x^2+4x+5
dx divide by (x^2+4*x+5)
Similar expressions
dx/(x^2+4*x-5)
dx/(x^2-4*x+5)

Solving integrals/ dx/(x^2+4*x+5)

Integral of dx/(x^2+4*x+5) dx

The solution

You have entered [src]

  1                
  /                
 |                 
 |       1         
 |  ------------ dx
 |   2             
 |  x  + 4*x + 5   
 |                 
/                  
0

\int\limits_{0}^{1} \frac{1}{\left(x^{2} + 4 x\right) + 5}\, dx

Integral(1/(x^2 + 4*x + 5), (x, 0, 1))

Detail solution

We have the integral:

  /               
 |                
 |      1         
 | ------------ dx
 |  2             
 | x  + 4*x + 5   
 |                
/

Rewrite the integrand

     1                 1        
------------ = -----------------
 2               /        2    \
x  + 4*x + 5   1*\(-x - 2)  + 1/

  /                 
 |                  
 |      1           
 | ------------ dx  
 |  2              =
 | x  + 4*x + 5     
 |                  
/

  /                
 |                 
 |       1         
 | ------------- dx
 |         2       
 | (-x - 2)  + 1   
 |                 
/

In the integral

  /                
 |                 
 |       1         
 | ------------- dx
 |         2       
 | (-x - 2)  + 1   
 |                 
/

do replacement

v = -2 - x

then

the integral =

  /                   
 |                    
 |   1                
 | ------ dv = atan(v)
 |      2             
 | 1 + v              
 |                    
/

do backward replacement

  /                              
 |                               
 |       1                       
 | ------------- dx = atan(2 + x)
 |         2                     
 | (-x - 2)  + 1                 
 |                               
/

Solution is:

C + atan(2 + x)

The answer (Indefinite) [src]

  /                                 
 |                                  
 |      1                           
 | ------------ dx = C + atan(2 + x)
 |  2                               
 | x  + 4*x + 5                     
 |                                  
/

\int \frac{1}{\left(x^{2} + 4 x\right) + 5}\, dx = C + \operatorname{atan}{\left(x + 2 \right)}

Simplify

The graph

Plot the graph f(x)

The answer [src]

-atan(2) + atan(3)

- \operatorname{atan}{\left(2 \right)} + \operatorname{atan}{\left(3 \right)}

-atan(2) + atan(3)

- \operatorname{atan}{\left(2 \right)} + \operatorname{atan}{\left(3 \right)}

-atan(2) + atan(3)

Numerical answer [src]

0.141897054604164

0.141897054604164

The graph

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

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Identical expressions

Similar expressions

Integral of dx/(x^2+4*x+5) dx

Limits of integration:

The graph:

Piecewise:

The solution