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(xdx)/((x+1)*(2x+1))
Solving integrals/ (xdx)/((x+1)*(2x+1))

Integral of (xdx)/((x+1)*(2x+1)) 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           
 |  ----------------- dx
 |  (x + 1)*(2*x + 1)   
 |                      
/                       
0
∫01x(x+1)(2x+1) dx\int\limits_{0}^{1} \frac{x}{\left(x + 1\right) \left(2 x + 1\right)}\, dx 
Integral(x/(((x + 1)*(2*x + 1))), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                    
 |                                                     
 |         x                  log(1 + 2*x)             
 | ----------------- dx = C - ------------ + log(1 + x)
 | (x + 1)*(2*x + 1)               2                   
 |                                                     
/
∫x(x+1)(2x+1) dx=C+log⁡(x+1)−log⁡(2x+1)2\int \frac{x}{\left(x + 1\right) \left(2 x + 1\right)}\, dx = C + \log{\left(x + 1 \right)} - \frac{\log{\left(2 x + 1 \right)}}{2}
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] 
log(2)   log(3/2)
------ - --------
  2         2
−log⁡(32)2+log⁡(2)2- \frac{\log{\left(\frac{3}{2} \right)}}{2} + \frac{\log{\left(2 \right)}}{2} 
=
= 
log(2)   log(3/2)
------ - --------
  2         2
−log⁡(32)2+log⁡(2)2- \frac{\log{\left(\frac{3}{2} \right)}}{2} + \frac{\log{\left(2 \right)}}{2} 
log(2)/2 - log(3/2)/2
Numerical answer [src] 
0.14384103622589
0.14384103622589
The graph
Integral of (xdx)/((x+1)*(2x+1)) dx

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

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