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Solving integrals/ x/(x+y)^3

Integral of x/(x+y)^3 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1            
  /            
 |             
 |     x       
 |  -------- dx
 |         3   
 |  (x + y)    
 |             
/              
0
$$\int\limits_{0}^{1} \frac{x}{\left(x + y\right)^{3}}\, dx$$ 
Integral(x/(x + y)^3, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                    
 |                                     
 |    x                1         y     
 | -------- dx = C - ----- + ----------
 |        3          x + y            2
 | (x + y)                   2*(x + y) 
 |                                     
/
$$\int \frac{x}{\left(x + y\right)^{3}}\, dx = C + \frac{y}{2 \left(x + y\right)^{2}} - \frac{1}{x + y}$$
Simplify
The answer [src] 
 1        2 + y     
--- - --------------
2*y          2      
      2 + 2*y  + 4*y
$$- \frac{y + 2}{2 y^{2} + 4 y + 2} + \frac{1}{2 y}$$ 
=
= 
 1        2 + y     
--- - --------------
2*y          2      
      2 + 2*y  + 4*y
$$- \frac{y + 2}{2 y^{2} + 4 y + 2} + \frac{1}{2 y}$$ 
1/(2*y) - (2 + y)/(2 + 2*y^2 + 4*y)

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

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