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Identical expressions
(x^ two - forty-nine)^ two
(x squared minus 49) squared
(x to the power of two minus forty minus nine) to the power of two
(x2-49)2
x2-492
(x²-49)²
(x to the power of 2-49) to the power of 2
x^2-49^2
(x^2-49)^2dx
Similar expressions
(x^2+49)^2

Integral of (x^2-49)^2 dx

The solution

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  1              
  /              
 |               
 |           2   
 |  / 2     \    
 |  \x  - 49/  dx
 |               
/                
0

$$\int\limits_{0}^{1} \left(x^{2} - 49\right)^{2}\, dx$$

Integral((x^2 - 49)^2, (x, 0, 1))

Detail solution

Rewrite the integrand:

$\left(x^{2} - 49\right)^{2} = x^{4} - 98 x^{2} + 2401$
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:
  
  $\int \left(- 98 x^{2}\right)\, dx = - 98 \int x^{2}\, dx$
  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: $- \frac{98 x^{3}}{3}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 2401\, dx = 2401 x$
The result is: $\frac{x^{5}}{5} - \frac{98 x^{3}}{3} + 2401 x$
Now simplify:

$\frac{x \left(3 x^{4} - 490 x^{2} + 36015\right)}{15}$
Add the constant of integration:

$\frac{x \left(3 x^{4} - 490 x^{2} + 36015\right)}{15}+ \mathrm{constant}$

The answer is:

$\frac{x \left(3 x^{4} - 490 x^{2} + 36015\right)}{15}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                       
 |                                        
 |          2                       3    5
 | / 2     \                    98*x    x 
 | \x  - 49/  dx = C + 2401*x - ----- + --
 |                                3     5 
/

$$\int \left(x^{2} - 49\right)^{2}\, dx = C + \frac{x^{5}}{5} - \frac{98 x^{3}}{3} + 2401 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

35528
-----
  15

$$\frac{35528}{15}$$

35528
-----
  15

$$\frac{35528}{15}$$

35528/15

Numerical answer [src]

2368.53333333333

2368.53333333333

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

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Integral of (x^2-49)^2 dx

Limits of integration:

The graph:

Piecewise:

The solution