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1/(1+x^2)^2

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1             
  /             
 |              
 |      1       
 |  --------- dx
 |          2   
 |  /     2\    
 |  \1 + x /    
 |              
/               
0               
$$\int\limits_{0}^{1} \frac{1}{\left(x^{2} + 1\right)^{2}}\, dx$$
Integral(1/((1 + x^2)^2), (x, 0, 1))
Detail solution

    TrigSubstitutionRule(theta=_theta, func=tan(_theta), rewritten=cos(_theta)**2, substep=RewriteRule(rewritten=cos(2*_theta)/2 + 1/2, substep=AddRule(substeps=[ConstantTimesRule(constant=1/2, other=cos(2*_theta), substep=URule(u_var=_u, u_func=2*_theta, constant=1/2, substep=ConstantTimesRule(constant=1/2, other=cos(_u), substep=TrigRule(func='cos', arg=_u, context=cos(_u), symbol=_u), context=cos(_u), symbol=_u), context=cos(2*_theta), symbol=_theta), context=cos(2*_theta)/2, symbol=_theta), ConstantRule(constant=1/2, context=1/2, symbol=_theta)], context=cos(2*_theta)/2 + 1/2, symbol=_theta), context=cos(_theta)**2, symbol=_theta), restriction=True, context=1/((x**2 + 1)**2), symbol=x)

  1. Now simplify:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                       
 |                                        
 |     1              atan(x)       x     
 | --------- dx = C + ------- + ----------
 |         2             2        /     2\
 | /     2\                     2*\1 + x /
 | \1 + x /                               
 |                                        
/                                         
$$\int \frac{1}{\left(x^{2} + 1\right)^{2}}\, dx = C + \frac{x}{2 \left(x^{2} + 1\right)} + \frac{\operatorname{atan}{\left(x \right)}}{2}$$
The graph
The answer [src]
1   pi
- + --
4   8 
$$\frac{1}{4} + \frac{\pi}{8}$$
=
=
1   pi
- + --
4   8 
$$\frac{1}{4} + \frac{\pi}{8}$$
1/4 + pi/8
Numerical answer [src]
0.642699081698724
0.642699081698724
The graph
Integral of 1/(1+x^2)^2 dx

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