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Integral of (4x-10)/((x+2)(x²-2x+10)) dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src]
  1                           
  /                           
 |                            
 |          4*x - 10          
 |  ----------------------- dx
 |          / 2           \   
 |  (x + 2)*\x  - 2*x + 10/   
 |                            
/                             
0                             
$$\int\limits_{0}^{1} \frac{4 x - 10}{\left(x + 2\right) \left(\left(x^{2} - 2 x\right) + 10\right)}\, dx$$
Integral((4*x - 10)/(((x + 2)*(x^2 - 2*x + 10))), (x, 0, 1))
The answer (Indefinite) [src]
  /                                                                       /  1   x\
 |                                     /      2      \                atan|- - + -|
 |         4*x - 10                 log\10 + x  - 2*x/                    \  3   3/
 | ----------------------- dx = C + ------------------ - log(2 + x) + -------------
 |         / 2           \                  2                               3      
 | (x + 2)*\x  - 2*x + 10/                                                         
 |                                                                                 
/                                                                                  
$$\int \frac{4 x - 10}{\left(x + 2\right) \left(\left(x^{2} - 2 x\right) + 10\right)}\, dx = C - \log{\left(x + 2 \right)} + \frac{\log{\left(x^{2} - 2 x + 10 \right)}}{2} + \frac{\operatorname{atan}{\left(\frac{x}{3} - \frac{1}{3} \right)}}{3}$$
The graph
The answer [src]
log(9)            log(10)   atan(1/3)         
------ - log(3) - ------- + --------- + log(2)
  2                  2          3             
$$- \frac{\log{\left(10 \right)}}{2} - \log{\left(3 \right)} + \frac{\operatorname{atan}{\left(\frac{1}{3} \right)}}{3} + \log{\left(2 \right)} + \frac{\log{\left(9 \right)}}{2}$$
=
=
log(9)            log(10)   atan(1/3)         
------ - log(3) - ------- + --------- + log(2)
  2                  2          3             
$$- \frac{\log{\left(10 \right)}}{2} - \log{\left(3 \right)} + \frac{\operatorname{atan}{\left(\frac{1}{3} \right)}}{3} + \log{\left(2 \right)} + \frac{\log{\left(9 \right)}}{2}$$
log(9)/2 - log(3) - log(10)/2 + atan(1/3)/3 + log(2)
Numerical answer [src]
-0.350895181138197
-0.350895181138197

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