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x^4/(x^3-1)
Solving integrals/ x^4/(x^3-1)

Integral of x^4/(x^3-1) dx

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The solution

You have entered [src] 
  1          
  /          
 |           
 |     4     
 |    x      
 |  ------ dx
 |   3       
 |  x  - 1   
 |           
/            
0
∫01x4x3−1 dx\int\limits_{0}^{1} \frac{x^{4}}{x^{3} - 1}\, dx 
Integral(x^4/(x^3 - 1), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                               /    ___          \
 |                                                        ___     |2*\/ 3 *(1/2 + x)|
 |    4             2      /         2\                 \/ 3 *atan|-----------------|
 |   x             x    log\1 + x + x /   log(-1 + x)             \        3        /
 | ------ dx = C + -- - --------------- + ----------- + -----------------------------
 |  3              2           6               3                      3              
 | x  - 1                                                                            
 |                                                                                   
/
∫x4x3−1 dx=C+x22+log⁡(x−1)3−log⁡(x2+x+1)6+3atan⁡(23(x+12)3)3\int \frac{x^{4}}{x^{3} - 1}\, dx = C + \frac{x^{2}}{2} + \frac{\log{\left(x - 1 \right)}}{3} - \frac{\log{\left(x^{2} + x + 1 \right)}}{6} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \left(x + \frac{1}{2}\right)}{3} \right)}}{3}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-50005000
Plot the graph f(x)
The answer [src] 
      pi*I
-oo - ----
       3
−∞−iπ3-\infty - \frac{i \pi}{3} 
=
= 
      pi*I
-oo - ----
       3
−∞−iπ3-\infty - \frac{i \pi}{3} 
-oo - pi*i/3
Numerical answer [src] 
-14.0777877494774
-14.0777877494774
The graph
Integral of x^4/(x^3-1) dx

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

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