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

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  2              
  /              
 |               
 |     x*x       
 |  ---------- dx
 |           2   
 |  (2*x + 1)    
 |               
/                
1
$$\int\limits_{1}^{2} \frac{x x}{\left(2 x + 1\right)^{2}}\, dx$$ 
Integral((x*x)/(2*x + 1)^2, (x, 1, 2))
The answer (Indefinite) [src] 
  /                                                  
 |                                                   
 |    x*x              log(1 + 2*x)        1        x
 | ---------- dx = C - ------------ - ----------- + -
 |          2               4         8*(1 + 2*x)   4
 | (2*x + 1)                                         
 |                                                   
/
$$\int \frac{x x}{\left(2 x + 1\right)^{2}}\, dx = C + \frac{x}{4} - \frac{\log{\left(2 x + 1 \right)}}{4} - \frac{1}{8 \left(2 x + 1\right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
4    log(5)   log(3)
-- - ------ + ------
15     4        4
$$- \frac{\log{\left(5 \right)}}{4} + \frac{4}{15} + \frac{\log{\left(3 \right)}}{4}$$ 
=
= 
4    log(5)   log(3)
-- - ------ + ------
15     4        4
$$- \frac{\log{\left(5 \right)}}{4} + \frac{4}{15} + \frac{\log{\left(3 \right)}}{4}$$ 
4/15 - log(5)/4 + log(3)/4
Numerical answer [src] 
0.138960260725169
0.138960260725169

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

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