Mister Exam

Other calculators


x^3/(x-1)

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  2. Integrate term-by-term:

    1. The integral of is when :

    1. The integral of is when :

    1. The integral of a constant is the constant times the variable of integration:

    1. Let .

      Then let and substitute :

      1. The integral of is .

      Now substitute back in:

    The result is:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                        
 |                                         
 |    3                2    3              
 |   x                x    x               
 | ----- dx = C + x + -- + -- + log(-1 + x)
 | x - 1              2    3               
 |                                         
/                                          
$$\int \frac{x^{3}}{x - 1}\, dx = C + \frac{x^{3}}{3} + \frac{x^{2}}{2} + x + \log{\left(x - 1 \right)}$$
The graph
The answer [src]
-oo - pi*I
$$-\infty - i \pi$$
=
=
-oo - pi*I
$$-\infty - i \pi$$
-oo - pi*i
Numerical answer [src]
-42.2576234528862
-42.2576234528862
The graph
Integral of x^3/(x-1) dx

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