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-x^2-2x+3
Solving integrals/ -x^2-2x+3

Integral of -x^2-2x+3 dx

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The solution

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∫02((−x2−2x)+3) dx\int\limits_{0}^{2} \left(\left(- x^{2} - 2 x\right) + 3\right)\, dx 
Integral(-x^2 - 2*x + 3, (x, 0, 2))
Detail solution

  1. Integrate term-by-term:

    1. Integrate term-by-term:

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

        ∫(−x2) dx=−∫x2 dx\int \left(- x^{2}\right)\, dx = - \int x^{2}\, dx

        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}

        So, the result is: −x33- \frac{x^{3}}{3}

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

        ∫(−2x) dx=−2∫x dx\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 n≠−1n \neq -1:

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

        So, the result is: −x2- x^{2}

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

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

      ∫3 dx=3x\int 3\, dx = 3 x

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

  2. Now simplify:

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

  3. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
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 | \- x  - 2*x + 3/ dx = C - x  + 3*x - --
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∫((−x2−2x)+3) dx=C−x33−x2+3x\int \left(\left(- x^{2} - 2 x\right) + 3\right)\, dx = C - \frac{x^{3}}{3} - x^{2} + 3 x
Simplify
The graph
0.02.00.20.40.60.81.01.21.41.61.8-1010
Plot the graph f(x)
The answer [src] 
-2/3
−23- \frac{2}{3} 
=
= 
-2/3
−23- \frac{2}{3} 
-2/3
Numerical answer [src] 
-0.666666666666667
-0.666666666666667
The graph
Integral of -x^2-2x+3 dx

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

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