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x^3-3*x
Solving integrals/ x^3-3*x

Integral of x^3-3*x dx

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The solution

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∫01(x3−3x) dx\int\limits_{0}^{1} \left(x^{3} - 3 x\right)\, dx 
Integral(x^3 - 3*x, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫x3 dx=x44\int x^{3}\, dx = \frac{x^{4}}{4}

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

      ∫(−3x) dx=−3∫x dx\int \left(- 3 x\right)\, dx = - 3 \int x\, dx

      1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

        ∫x dx=x22\int x\, dx = \frac{x^{2}}{2}

      So, the result is: −3x22- \frac{3 x^{2}}{2}

    The result is: x44−3x22\frac{x^{4}}{4} - \frac{3 x^{2}}{2}

  2. Now simplify:

    x2(x2−6)4\frac{x^{2} \left(x^{2} - 6\right)}{4}

  3. Add the constant of integration:

    x2(x2−6)4+constant\frac{x^{2} \left(x^{2} - 6\right)}{4}+ \mathrm{constant}

The answer is:

x2(x2−6)4+constant\frac{x^{2} \left(x^{2} - 6\right)}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                             
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 | \x  - 3*x/ dx = C - ---- + --
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∫(x3−3x) dx=C+x44−3x22\int \left(x^{3} - 3 x\right)\, dx = C + \frac{x^{4}}{4} - \frac{3 x^{2}}{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.902-4
Plot the graph f(x)
The answer [src] 
-5/4
−54- \frac{5}{4} 
=
= 
-5/4
−54- \frac{5}{4} 
-5/4
Numerical answer [src] 
-1.25
-1.25
The graph
Integral of x^3-3*x dx

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

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