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x^2-6x-7
Solving integrals/ x^2-6x-7

Integral of x^2-6x-7 dx

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The solution

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∫−17((x2−6x)−7) dx\int\limits_{-1}^{7} \left(\left(x^{2} - 6 x\right) - 7\right)\, dx 
Integral(x^2 - 6*x - 7, (x, -1, 7))
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:

        ∫x2 dx=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=−6∫x dx\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 n≠−1n \neq -1:

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

        So, the result is: −3x2- 3 x^{2}

      The result is: x33−3x2\frac{x^{3}}{3} - 3 x^{2}

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

      ∫(−7) dx=−7x\int \left(-7\right)\, dx = - 7 x

    The result is: x33−3x2−7x\frac{x^{3}}{3} - 3 x^{2} - 7 x

  2. Now simplify:

    x(x2−9x−21)3\frac{x \left(x^{2} - 9 x - 21\right)}{3}

  3. Add the constant of integration:

    x(x2−9x−21)3+constant\frac{x \left(x^{2} - 9 x - 21\right)}{3}+ \mathrm{constant}

The answer is:

x(x2−9x−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 - 7*x - 3*x  + --
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∫((x2−6x)−7) dx=C+x33−3x2−7x\int \left(\left(x^{2} - 6 x\right) - 7\right)\, dx = C + \frac{x^{3}}{3} - 3 x^{2} - 7 x
Simplify
The graph
7.00.01.02.03.04.05.06.0-1.0-100100
Plot the graph f(x)
The answer [src] 
-256/3
−2563- \frac{256}{3} 
=
= 
-256/3
−2563- \frac{256}{3} 
-256/3
Numerical answer [src] 
-85.3333333333333
-85.3333333333333
The graph
Integral of x^2-6x-7 dx

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

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