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x*arctg^2x
Solving integrals/ x*arctg^2x

Integral of x*arctg^2x dx

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The solution

You have entered [src] 
  1              
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 |        2      
 |  x*atan (x) dx
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0
∫01xatan⁡2(x) dx\int\limits_{0}^{1} x \operatorname{atan}^{2}{\left(x \right)}\, dx 
Integral(x*atan(x)^2, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                    
 |                         2         /     2\    2     2               
 |       2             atan (x)   log\1 + x /   x *atan (x)            
 | x*atan (x) dx = C + -------- + ----------- + ----------- - x*atan(x)
 |                        2            2             2                 
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log⁡(x2+1)−arctan⁡2x2+x2 arctan⁡2x2−(x−arctan⁡x) arctan⁡x{{\log \left(x^2+1\right)-\arctan ^2x}\over{2}}+{{x^2\,\arctan ^2x }\over{2}}-\left(x-\arctan x\right)\,\arctan x
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.01.0
Plot the graph f(x)
The answer [src] 
                2
log(2)   pi   pi 
------ - -- + ---
  2      4     16
8 log⁡2+π2−4 π16{{8\,\log 2+\pi^2-4\,\pi}\over{16}} 
=
= 
                2
log(2)   pi   pi 
------ - -- + ---
  2      4     16
−π4+log⁡(2)2+π216- \frac{\pi}{4} + \frac{\log{\left(2 \right)}}{2} + \frac{\pi^{2}}{16}
Упростить
Numerical answer [src] 
0.178025701950609
0.178025701950609
The graph
Integral of x*arctg^2x dx

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

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