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Derivative of:
1/(1+x^2)^2
Identical expressions
one /(one +x^ two)^ two
1 divide by (1 plus x squared ) squared
one divide by (one plus x to the power of two) to the power of two
1/(1+x2)2
1/1+x22
1/(1+x²)²
1/(1+x to the power of 2) to the power of 2
1/1+x^2^2
1 divide by (1+x^2)^2
1/(1+x^2)^2dx
Similar expressions
1/(1-x^2)^2

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

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

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)

Now simplify:

$\frac{x + \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}}{2 \left(x^{2} + 1\right)}$
Add the constant of integration:

$\frac{x + \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}}{2 \left(x^{2} + 1\right)}+ \mathrm{constant}$

The answer is:

$\frac{x + \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}}{2 \left(x^{2} + 1\right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

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

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

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Identical expressions

Similar expressions

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

Limits of integration:

The graph:

Piecewise:

The solution