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Integral of (3-x^2)^3
Identical expressions
(three -x^ two)^ three
(3 minus x squared ) cubed
(three minus x to the power of two) to the power of three
(3-x2)3
3-x23
(3-x²)³
(3-x to the power of 2) to the power of 3
3-x^2^3
(3-x^2)^3dx
Similar expressions
(3+x^2)^3

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

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

The solution

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

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

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

Detail solution

Rewrite the integrand:

$\left(3 - x^{2}\right)^{3} = - x^{6} + 9 x^{4} - 27 x^{2} + 27$
Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- x^{6}\right)\, dx = - \int x^{6}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{6}\, dx = \frac{x^{7}}{7}$
  So, the result is: $- \frac{x^{7}}{7}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 9 x^{4}\, dx = 9 \int x^{4}\, dx$
  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: $\frac{9 x^{5}}{5}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 27 x^{2}\right)\, dx = - 27 \int x^{2}\, dx$
  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: $- 9 x^{3}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 27\, dx = 27 x$
The result is: $- \frac{x^{7}}{7} + \frac{9 x^{5}}{5} - 9 x^{3} + 27 x$
Now simplify:

$\frac{x \left(- 5 x^{6} + 63 x^{4} - 315 x^{2} + 945\right)}{35}$
Add the constant of integration:

$\frac{x \left(- 5 x^{6} + 63 x^{4} - 315 x^{2} + 945\right)}{35}+ \mathrm{constant}$

The answer is:

$\frac{x \left(- 5 x^{6} + 63 x^{4} - 315 x^{2} + 945\right)}{35}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                          
 |                                           
 |         3                         7      5
 | /     2\              3          x    9*x 
 | \3 - x /  dx = C - 9*x  + 27*x - -- + ----
 |                                  7     5  
/

$$\int \left(3 - x^{2}\right)^{3}\, dx = C - \frac{x^{7}}{7} + \frac{9 x^{5}}{5} - 9 x^{3} + 27 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

688
---
 35

$$\frac{688}{35}$$

688
---
 35

$$\frac{688}{35}$$

688/35

Numerical answer [src]

19.6571428571429

19.6571428571429

The graph

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

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

Limits of integration:

The graph:

Piecewise:

The solution