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Integral of d{x}:
Integral of x^2sen(x)
Integral of t+1
Integral of (4-x^2)^2
Integral of 2*x/(x-1)
Canonical form:
(4-x^2)^2
Identical expressions
(four -x^ two)^ two
(4 minus x squared ) squared
(four minus x to the power of two) to the power of two
(4-x2)2
4-x22
(4-x²)²
(4-x to the power of 2) to the power of 2
4-x^2^2
(4-x^2)^2dx
Similar expressions
(4+x^2)^2

Solving integrals/ (4-x^2)^2

Integral of (4-x^2)^2 dx

The solution

You have entered [src]

  1             
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 |          2   
 |  /     2\    
 |  \4 - x /  dx
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0

$$\int\limits_{0}^{1} \left(4 - x^{2}\right)^{2}\, dx$$

Integral((4 - x^2)^2, (x, 0, 1))

Detail solution

Rewrite the integrand:

$\left(4 - x^{2}\right)^{2} = x^{4} - 8 x^{2} + 16$
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:
  
  $\int \left(- 8 x^{2}\right)\, dx = - 8 \int x^{2}\, dx$
  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: $- \frac{8 x^{3}}{3}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 16\, dx = 16 x$
The result is: $\frac{x^{5}}{5} - \frac{8 x^{3}}{3} + 16 x$
Now simplify:

$\frac{x \left(3 x^{4} - 40 x^{2} + 240\right)}{15}$
Add the constant of integration:

$\frac{x \left(3 x^{4} - 40 x^{2} + 240\right)}{15}+ \mathrm{constant}$

The answer is:

$\frac{x \left(3 x^{4} - 40 x^{2} + 240\right)}{15}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                   
 |                                    
 |         2                    3    5
 | /     2\                  8*x    x 
 | \4 - x /  dx = C + 16*x - ---- + --
 |                            3     5 
/

$$\int \left(4 - x^{2}\right)^{2}\, dx = C + \frac{x^{5}}{5} - \frac{8 x^{3}}{3} + 16 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

203
---
 15

$$\frac{203}{15}$$

203
---
 15

$$\frac{203}{15}$$

203/15

Numerical answer [src]

13.5333333333333

13.5333333333333

The graph

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

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Integral of (4-x^2)^2 dx

Limits of integration:

The graph:

Piecewise:

The solution