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(x+20)/(x^3-8)

Integral of (x+20)/(x^3-8) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
  1          
  /          
 |           
 |  x + 20   
 |  ------ dx
 |   3       
 |  x  - 8   
 |           
/            
0            
$$\int\limits_{0}^{1} \frac{x + 20}{x^{3} - 8}\, dx$$
Integral((x + 20)/(x^3 - 8), (x, 0, 1))
The answer (Indefinite) [src]
                                                                       /  ___        \
  /                                                            ___     |\/ 3 *(1 + x)|
 |                       /     2      \                    3*\/ 3 *atan|-------------|
 | x + 20          11*log\4 + x  + 2*x/   11*log(-2 + x)               \      3      /
 | ------ dx = C - -------------------- + -------------- - ---------------------------
 |  3                       12                  6                       2             
 | x  - 8                                                                             
 |                                                                                    
/                                                                                     
$$\int \frac{x + 20}{x^{3} - 8}\, dx = C + \frac{11 \log{\left(x - 2 \right)}}{6} - \frac{11 \log{\left(x^{2} + 2 x + 4 \right)}}{12} - \frac{3 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(x + 1\right)}{3} \right)}}{2}$$
The graph
The answer [src]
                                                  /    ___\           
                                          ___     |2*\/ 3 |           
                                      3*\/ 3 *atan|-------|        ___
  11*log(2)   11*log(7)   11*log(4)               \   3   /   pi*\/ 3 
- --------- - --------- + --------- - --------------------- + --------
      6           12          12                2                4    
$$- \frac{3 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3}}{3} \right)}}{2} - \frac{11 \log{\left(7 \right)}}{12} - \frac{11 \log{\left(2 \right)}}{6} + \frac{11 \log{\left(4 \right)}}{12} + \frac{\sqrt{3} \pi}{4}$$
=
=
                                                  /    ___\           
                                          ___     |2*\/ 3 |           
                                      3*\/ 3 *atan|-------|        ___
  11*log(2)   11*log(7)   11*log(4)               \   3   /   pi*\/ 3 
- --------- - --------- + --------- - --------------------- + --------
      6           12          12                2                4    
$$- \frac{3 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3}}{3} \right)}}{2} - \frac{11 \log{\left(7 \right)}}{12} - \frac{11 \log{\left(2 \right)}}{6} + \frac{11 \log{\left(4 \right)}}{12} + \frac{\sqrt{3} \pi}{4}$$
-11*log(2)/6 - 11*log(7)/12 + 11*log(4)/12 - 3*sqrt(3)*atan(2*sqrt(3)/3)/2 + pi*sqrt(3)/4
Numerical answer [src]
-2.65013968591938
-2.65013968591938
The graph
Integral of (x+20)/(x^3-8) dx

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