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Solving integrals/ x^3-3x+1

Integral of x^3-3x+1 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                  
  /                  
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 |  / 3          \   
 |  \x  - 3*x + 1/ dx
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0
$$\int\limits_{0}^{1} \left(\left(x^{3} - 3 x\right) + 1\right)\, dx$$ 
Integral(x^3 - 3*x + 1, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    1. Integrate term-by-term:

      1. The integral of is when :

      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:

      The result is:

    1. The integral of a constant is the constant times the variable of integration:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                     
 |                                2    4
 | / 3          \              3*x    x 
 | \x  - 3*x + 1/ dx = C + x - ---- + --
 |                              2     4 
/
$$\int \left(\left(x^{3} - 3 x\right) + 1\right)\, dx = C + \frac{x^{4}}{4} - \frac{3 x^{2}}{2} + x$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
-1/4
$$- \frac{1}{4}$$ 
=
= 
-1/4
$$- \frac{1}{4}$$ 
-1/4
Numerical answer [src] 
-0.25
-0.25

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

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