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

You entered:

x^3/(x^4-x^3)

What you mean?

x^3/(x^4 - x^3)
 
x^3*3/(x^4 - x)
 
x^3/((x^4 - x)^3)
 
x^3/(x^4) - x^3
 
x^3*4/x - x^3
 
x^3/(x^4) - x^3
 
x^3/(x^4) - x^3

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1           
  /           
 |            
 |      3     
 |     x      
 |  ------- dx
 |   4    3   
 |  x  - x    
 |            
/             
0
$$\int\limits_{0}^{1} \frac{x^{3}}{x^{4} - x^{3}}\, dx$$ 
Integral(x^3/(x^4 - x^3), (x, 0, 1))
Detail solution

  1. There are multiple ways to do this integral.

    Method #1

    1. Rewrite the integrand:

    2. Let .

      Then let and substitute :

      1. The integral of is .

      Now substitute back in:

    Method #2

    1. Rewrite the integrand:

    2. Let .

      Then let and substitute :

      1. The integral of is .

      Now substitute back in:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                            
 |                             
 |     3                       
 |    x                        
 | ------- dx = C + log(-1 + x)
 |  4    3                     
 | x  - x                      
 |                             
/
$$\int \frac{x^{3}}{x^{4} - x^{3}}\, dx = C + \log{\left(x - 1 \right)}$$
Simplify
The answer [src] 
-oo - pi*I
$$-\infty - i \pi$$ 
=
= 
-oo - pi*I
$$-\infty - i \pi$$
Упростить
Numerical answer [src] 
-44.0909567862201
-44.0909567862201

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

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