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xlnx/(1+x²)²
Solving integrals/ xlnx/(1+x²)²

Integral of xlnx/(1+x²)² dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
  1             
  /             
 |              
 |   x*log(x)   
 |  --------- dx
 |          2   
 |  /     2\    
 |  \1 + x /    
 |              
/               
0
∫01xlog⁡(x)(x2+1)2 dx\int\limits_{0}^{1} \frac{x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}\, dx 
Integral((x*log(x))/(1 + x^2)^2, (x, 0, 1))
The answer (Indefinite) [src] 
                         /    1 \             
  /                   log|1 + --|             
 |                       |     2|             
 |  x*log(x)             \    x /     log(x)  
 | --------- dx = C - ----------- - ----------
 |         2               4          /     2\
 | /     2\                         2*\1 + x /
 | \1 + x /                                   
 |                                            
/
∫xlog⁡(x)(x2+1)2 dx=C−log⁡(1+1x2)4−log⁡(x)2(x2+1)\int \frac{x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}\, dx = C - \frac{\log{\left(1 + \frac{1}{x^{2}} \right)}}{4} - \frac{\log{\left(x \right)}}{2 \left(x^{2} + 1\right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.5-0.5
Plot the graph f(x)
The answer [src] 
-log(2) 
--------
   4
−log⁡(2)4- \frac{\log{\left(2 \right)}}{4} 
=
= 
-log(2) 
--------
   4
−log⁡(2)4- \frac{\log{\left(2 \right)}}{4} 
-log(2)/4
Numerical answer [src] 
-0.173286795139986
-0.173286795139986
The graph
Integral of xlnx/(1+x²)² dx

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

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