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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

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-3
∫−32(x2+x−6) dx\int\limits_{-3}^{2} \left(x^{2} + x - 6\right)\, dx 
Integral(x^2 + x - 1*6, (x, -3, 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:

      ∫x2 dx=x33\int x^{2}\, dx = \frac{x^{3}}{3}

    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}

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

      ∫((−1)6) dx=−6x\int \left(\left(-1\right) 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 
/
x33+x22−6 x{{x^3}\over{3}}+{{x^2}\over{2}}-6\,x
Simplify
The graph
-3.0-2.5-2.0-1.5-1.0-0.52.00.00.51.01.5-2525
Plot the graph f(x)
The answer [src] 
-125/6
−1256-{{125}\over{6}} 
=
= 
-125/6
−1256- \frac{125}{6}
Упростить
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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