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Integral of x^2-6x+7 dx

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The solution

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101((x26x)+7)dx\int\limits_{-10}^{-1} \left(\left(x^{2} - 6 x\right) + 7\right)\, dx
Integral(x^2 - 6*x + 7, (x, -10, -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:

        (6x)dx=6xdx\int \left(- 6 x\right)\, dx = - 6 \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: 3x2- 3 x^{2}

      The result is: x333x2\frac{x^{3}}{3} - 3 x^{2}

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

      7dx=7x\int 7\, dx = 7 x

    The result is: x333x2+7x\frac{x^{3}}{3} - 3 x^{2} + 7 x

  2. Now simplify:

    x(x29x+21)3\frac{x \left(x^{2} - 9 x + 21\right)}{3}

  3. Add the constant of integration:

    x(x29x+21)3+constant\frac{x \left(x^{2} - 9 x + 21\right)}{3}+ \mathrm{constant}


The answer is:

x(x29x+21)3+constant\frac{x \left(x^{2} - 9 x + 21\right)}{3}+ \mathrm{constant}

The answer (Indefinite) [src]
  /                                       
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 | \x  - 6*x + 7/ dx = C - 3*x  + 7*x + --
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((x26x)+7)dx=C+x333x2+7x\int \left(\left(x^{2} - 6 x\right) + 7\right)\, dx = C + \frac{x^{3}}{3} - 3 x^{2} + 7 x
The graph
-1.0-9.0-8.0-7.0-6.0-5.0-4.0-3.0-2.0-10.0-10001000
The answer [src]
693
693693
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=
693
693693
693
Numerical answer [src]
693.0
693.0

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