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Integral of d{x}:
Integral of k
Integral of -y
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Integral of (1-x^2)^(1/2)
Derivative of:
(x^2-1)^2
Graphing y =:
(x^2-1)^2
Identical expressions
(x^ two - one)^ two
(x squared minus 1) squared
(x to the power of two minus one) to the power of two
(x2-1)2
x2-12
(x²-1)²
(x to the power of 2-1) to the power of 2
x^2-1^2
(x^2-1)^2dx
Similar expressions
(x^2+1)^2

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

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

The solution

You have entered [src]

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

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

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

Detail solution

Rewrite the integrand:

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

$\frac{x^{5}}{5} - \frac{2 x^{3}}{3} + x+ \mathrm{constant}$

The answer is:

$\frac{x^{5}}{5} - \frac{2 x^{3}}{3} + x+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

8/15

$$\frac{8}{15}$$

8/15

$$\frac{8}{15}$$

8/15

Numerical answer [src]

0.533333333333333

0.533333333333333

The graph

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

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Identical expressions

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

Limits of integration:

The graph:

Piecewise:

The solution