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Solving integrals/ dx/((5x-1)^2+4)

Integral of dx/((5x-1)^2+4) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                  
  /                  
 |                   
 |        1          
 |  -------------- dx
 |           2       
 |  (5*x - 1)  + 4   
 |                   
/                    
0
$$\int\limits_{0}^{1} \frac{1}{\left(5 x - 1\right)^{2} + 4}\, dx$$ 
Integral(1/((5*x - 1)^2 + 4), (x, 0, 1))
The answer (Indefinite) [src] 
  /                            /  1   5*x\
 |                         atan|- - + ---|
 |       1                     \  2    2 /
 | -------------- dx = C + ---------------
 |          2                     10      
 | (5*x - 1)  + 4                         
 |                                        
/
$$\int \frac{1}{\left(5 x - 1\right)^{2} + 4}\, dx = C + \frac{\operatorname{atan}{\left(\frac{5 x}{2} - \frac{1}{2} \right)}}{10}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
atan(1/2)   atan(2)
--------- + -------
    10         10
$$\frac{\operatorname{atan}{\left(\frac{1}{2} \right)}}{10} + \frac{\operatorname{atan}{\left(2 \right)}}{10}$$ 
=
= 
atan(1/2)   atan(2)
--------- + -------
    10         10
$$\frac{\operatorname{atan}{\left(\frac{1}{2} \right)}}{10} + \frac{\operatorname{atan}{\left(2 \right)}}{10}$$ 
atan(1/2)/10 + atan(2)/10
Numerical answer [src] 
0.15707963267949
0.15707963267949

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

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