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Integral of d{x}:
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Derivative of:
x^3/(x-1)
Graphing y =:
x^3/(x-1)
Identical expressions
x^ three /(x- one)
x cubed divide by (x minus 1)
x to the power of three divide by (x minus one)
x3/(x-1)
x3/x-1
x³/(x-1)
x to the power of 3/(x-1)
x^3/x-1
x^3 divide by (x-1)
x^3/(x-1)dx
Similar expressions
(x^3)/((x-1)*(x+1)*(x+2))
x^3/(x+1)

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

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

The solution

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  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

Rewrite the integrand:

$\frac{x^{3}}{x - 1} = x^{2} + x + 1 + \frac{1}{x - 1}$
Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{2}\, dx = \frac{x^{3}}{3}$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x\, dx = \frac{x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, dx = x$
1. Let $u = x - 1$ .
  
  Then let $du = dx$ and substitute $du$ :
  
  $\int \frac{1}{u}\, du$
  1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
  Now substitute $u$ back in:
  
  $\log{\left(x - 1 \right)}$
The result is: $\frac{x^{3}}{3} + \frac{x^{2}}{2} + x + \log{\left(x - 1 \right)}$
Add the constant of integration:

$\frac{x^{3}}{3} + \frac{x^{2}}{2} + x + \log{\left(x - 1 \right)}+ \mathrm{constant}$

The answer is:

$\frac{x^{3}}{3} + \frac{x^{2}}{2} + x + \log{\left(x - 1 \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                        
 |                                         
 |    3                2    3              
 |   x                x    x               
 | ----- dx = C + x + -- + -- + log(-1 + x)
 | x - 1              2    3               
 |                                         
/

$$\int \frac{x^{3}}{x - 1}\, dx = C + \frac{x^{3}}{3} + \frac{x^{2}}{2} + x + \log{\left(x - 1 \right)}$$

Simplify

The graph

Plot the graph f(x)

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

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

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Identical expressions

Similar expressions

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

Limits of integration:

The graph:

Piecewise:

The solution