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32x^3-4x+

Integral of 32x^3-4x+ dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src]
 1/2                
  /                 
 |                  
 |  /    3      \   
 |  \32*x  - 4*x/ dx
 |                  
/                   
-1                  
$$\int\limits_{-1}^{\frac{1}{2}} \left(32 x^{3} - 4 x\right)\, dx$$
Integral(32*x^3 - 4*x, (x, -1, 1/2))
Detail solution
  1. Integrate term-by-term:

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. The integral of is when :

      So, the result is:

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. The integral of a constant times a function is the constant times the integral of the function:

        1. The integral of is when :

        So, the result is:

      So, the result is:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                  
 |                                   
 | /    3      \             2      4
 | \32*x  - 4*x/ dx = C - 2*x  + 8*x 
 |                                   
/                                    
$$8\,x^4-2\,x^2$$
The graph
The answer [src]
-6
$$-6$$
=
=
-6
$$-6$$
Numerical answer [src]
-6.0
-6.0
The graph
Integral of 32x^3-4x+ dx

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