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x^2-2x-1

Integral of x^2-2x-1 dx

Limits of integration:

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The graph:

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Piecewise:

The solution

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01((x22x)1)dx\int\limits_{0}^{1} \left(\left(x^{2} - 2 x\right) - 1\right)\, dx
Integral(x^2 - 2*x - 1, (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 n1n \neq -1:

        x2dx=x33\int x^{2}\, dx = \frac{x^{3}}{3}

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

        (2x)dx=2xdx\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 n1n \neq -1:

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

        So, the result is: x2- x^{2}

      The result is: x33x2\frac{x^{3}}{3} - x^{2}

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

      (1)dx=x\int \left(-1\right)\, dx = - x

    The result is: x33x2x\frac{x^{3}}{3} - x^{2} - x

  2. Now simplify:

    x(x23x1)x \left(\frac{x^{2}}{3} - x - 1\right)

  3. Add the constant of integration:

    x(x23x1)+constantx \left(\frac{x^{2}}{3} - x - 1\right)+ \mathrm{constant}


The answer is:

x(x23x1)+constantx \left(\frac{x^{2}}{3} - x - 1\right)+ \mathrm{constant}

The answer (Indefinite) [src]
  /                                   
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 | \x  - 2*x - 1/ dx = C - x - x  + --
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((x22x)1)dx=C+x33x2x\int \left(\left(x^{2} - 2 x\right) - 1\right)\, dx = C + \frac{x^{3}}{3} - x^{2} - x
The graph
0.001.000.100.200.300.400.500.600.700.800.902-4
The answer [src]
-5/3
53- \frac{5}{3}
=
=
-5/3
53- \frac{5}{3}
-5/3
Numerical answer [src]
-1.66666666666667
-1.66666666666667
The graph
Integral of x^2-2x-1 dx

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