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

Integral of x^2-x-6 dx

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The solution

You have entered [src] 
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-2
∫−23((x2−x)−6) dx\int\limits_{-2}^{3} \left(\left(x^{2} - x\right) - 6\right)\, dx 
Integral(x^2 - x - 6, (x, -2, 3))
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:

        ∫(−x) dx=−∫x dx\int \left(- x\right)\, dx = - \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: −x22- \frac{x^{2}}{2}

      The result is: x33−x22\frac{x^{3}}{3} - \frac{x^{2}}{2}

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

      ∫(−6) dx=−6x\int \left(-6\right)\, dx = - 6 x

    The result is: x33−x22−6x\frac{x^{3}}{3} - \frac{x^{2}}{2} - 6 x

  2. Now simplify:

    x(2x2−3x−36)6\frac{x \left(2 x^{2} - 3 x - 36\right)}{6}

  3. Add the constant of integration:

    x(2x2−3x−36)6+constant\frac{x \left(2 x^{2} - 3 x - 36\right)}{6}+ \mathrm{constant}

The answer is:

x(2x2−3x−36)6+constant\frac{x \left(2 x^{2} - 3 x - 36\right)}{6}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                   
 |                              2    3
 | / 2        \                x    x 
 | \x  - x - 6/ dx = C - 6*x - -- + --
 |                             2    3 
/
∫((x2−x)−6) dx=C+x33−x22−6x\int \left(\left(x^{2} - x\right) - 6\right)\, dx = C + \frac{x^{3}}{3} - \frac{x^{2}}{2} - 6 x
Simplify
The graph
-2.0-1.5-1.0-0.53.00.00.51.01.52.02.5-2525
Plot the graph f(x)
The answer [src] 
-125/6
−1256- \frac{125}{6} 
=
= 
-125/6
−1256- \frac{125}{6} 
-125/6
Numerical answer [src] 
-20.8333333333333
-20.8333333333333
The graph
Integral of x^2-x-6 dx

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

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