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x^2dx/(1+3x)^3
Solving integrals/ x^2dx/(1+3x)^3

Integral of x^2dx/(1+3x)^3 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1              
  /              
 |               
 |       2       
 |      x        
 |  ---------- dx
 |           3   
 |  (1 + 3*x)    
 |               
/                
0
$$\int\limits_{0}^{1} \frac{x^{2}}{\left(3 x + 1\right)^{3}}\, dx$$ 
Integral(x^2/(1 + 3*x)^3, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                               
 |                                                                
 |      2                                                         
 |     x                     1         log(1 + 3*x)        2      
 | ---------- dx = C - ------------- + ------------ + ------------
 |          3                      2        27        27*(1 + 3*x)
 | (1 + 3*x)           54*(1 + 3*x)                               
 |                                                                
/
$$\int \frac{x^{2}}{\left(3 x + 1\right)^{3}}\, dx = C + \frac{\log{\left(3 x + 1 \right)}}{27} + \frac{2}{27 \left(3 x + 1\right)} - \frac{1}{54 \left(3 x + 1\right)^{2}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
   11   log(4)
- --- + ------
  288     27
$$- \frac{11}{288} + \frac{\log{\left(4 \right)}}{27}$$ 
=
= 
   11   log(4)
- --- + ------
  288     27
$$- \frac{11}{288} + \frac{\log{\left(4 \right)}}{27}$$ 
-11/288 + log(4)/27
Numerical answer [src] 
0.0131497911525885
0.0131497911525885
The graph
Integral of x^2dx/(1+3x)^3 dx

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

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