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(x³-2x)
Solving integrals/ (x³-2x)

Integral of (x³-2x) dx

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The solution

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∫−12(x3−2x) dx\int\limits_{-1}^{2} \left(x^{3} - 2 x\right)\, dx 
Integral(x^3 - 2*x, (x, -1, 2))
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:

      ∫(−2x) dx=−2∫x dx\int \left(- 2 x\right)\, dx = - 2 \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: −x2- x^{2}

    The result is: x44−x2\frac{x^{4}}{4} - x^{2}

  2. Add the constant of integration:

    x44−x2+constant\frac{x^{4}}{4} - x^{2}+ \mathrm{constant}

The answer is:

x44−x2+constant\frac{x^{4}}{4} - x^{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫(x3−2x) dx=C+x44−x2\int \left(x^{3} - 2 x\right)\, dx = C + \frac{x^{4}}{4} - x^{2}
Simplify
The graph
-1.00-0.75-0.50-0.252.000.000.250.500.751.001.251.501.755-5
Plot the graph f(x)
The answer [src] 
3/4
34\frac{3}{4} 
=
= 
3/4
34\frac{3}{4} 
3/4
Numerical answer [src] 
0.75
0.75
The graph
Integral of (x³-2x) dx

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

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