Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x^(-1/2)
Integral of sin²xcos²x
Integral of x*2^(-x)
Integral of y^(-2/3)
Derivative of:
(x^2-1)^3
Graphing y =:
(x^2-1)^3
Identical expressions
(x^ two - one)^ three
(x squared minus 1) cubed
(x to the power of two minus one) to the power of three
(x2-1)3
x2-13
(x²-1)³
(x to the power of 2-1) to the power of 3
x^2-1^3
(x^2-1)^3dx
Similar expressions
(x^2+1)^3

Solving integrals/ (x^2-1)^3

Integral of (x^2-1)^3 dx

The solution

You have entered [src]

  1             
  /             
 |              
 |          3   
 |  / 2    \    
 |  \x  - 1/  dx
 |              
/               
0

$$\int\limits_{0}^{1} \left(x^{2} - 1\right)^{3}\, dx$$

Integral((x^2 - 1)^3, (x, 0, 1))

Detail solution

Rewrite the integrand:

$\left(x^{2} - 1\right)^{3} = x^{6} - 3 x^{4} + 3 x^{2} - 1$
Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{6}\, dx = \frac{x^{7}}{7}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 3 x^{4}\right)\, dx = - 3 \int x^{4}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{4}\, dx = \frac{x^{5}}{5}$
  So, the result is: $- \frac{3 x^{5}}{5}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 3 x^{2}\, dx = 3 \int x^{2}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{2}\, dx = \frac{x^{3}}{3}$
  So, the result is: $x^{3}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-1\right)\, dx = - x$
The result is: $\frac{x^{7}}{7} - \frac{3 x^{5}}{5} + x^{3} - x$
Add the constant of integration:

$\frac{x^{7}}{7} - \frac{3 x^{5}}{5} + x^{3} - x+ \mathrm{constant}$

The answer is:

$\frac{x^{7}}{7} - \frac{3 x^{5}}{5} + x^{3} - x+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                     
 |                                      
 |         3                      5    7
 | / 2    \            3       3*x    x 
 | \x  - 1/  dx = C + x  - x - ---- + --
 |                              5     7 
/

$$\int \left(x^{2} - 1\right)^{3}\, dx = C + \frac{x^{7}}{7} - \frac{3 x^{5}}{5} + x^{3} - x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-16 
----
 35

$$- \frac{16}{35}$$

-16 
----
 35

$$- \frac{16}{35}$$

-16/35

Numerical answer [src]

-0.457142857142857

-0.457142857142857

The graph

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (x^2-1)^3 dx

Limits of integration:

The graph:

Piecewise:

The solution