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x^3-3x+2
Solving integrals/ x^3-3x+2

Integral of x^3-3x+2 dx

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The solution

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∫01((x3−3x)+2) dx\int\limits_{0}^{1} \left(\left(x^{3} - 3 x\right) + 2\right)\, dx 
Integral(x^3 - 3*x + 2, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    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}

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

      ∫2 dx=2x\int 2\, dx = 2 x

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

  2. Now simplify:

    x(x3−6x+8)4\frac{x \left(x^{3} - 6 x + 8\right)}{4}

  3. Add the constant of integration:

    x(x3−6x+8)4+constant\frac{x \left(x^{3} - 6 x + 8\right)}{4}+ \mathrm{constant}

The answer is:

x(x3−6x+8)4+constant\frac{x \left(x^{3} - 6 x + 8\right)}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | \x  - 3*x + 2/ dx = C + 2*x - ---- + --
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∫((x3−3x)+2) dx=C+x44−3x22+2x\int \left(\left(x^{3} - 3 x\right) + 2\right)\, dx = C + \frac{x^{4}}{4} - \frac{3 x^{2}}{2} + 2 x
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9004
Plot the graph f(x)
The answer [src] 
3/4
34\frac{3}{4} 
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= 
3/4
34\frac{3}{4} 
3/4
Numerical answer [src] 
0.75
0.75
The graph
Integral of x^3-3x+2 dx

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

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