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Solving integrals/ 2*x+x^2

Integral of 2*x+x^2 dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

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∫0−2(x2+2x) dx\int\limits_{0}^{-2} \left(x^{2} + 2 x\right)\, dx 
Integral(2*x + x^2, (x, 0, -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 a constant times a function is the constant times the integral of the function:

      ∫2x dx=2∫x dx\int 2 x\, 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: x2x^{2}

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

  2. Now simplify:

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

  3. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
  /                           
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 | /       2\           2   x 
 | \2*x + x / dx = C + x  + --
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∫(x2+2x) dx=C+x33+x2\int \left(x^{2} + 2 x\right)\, dx = C + \frac{x^{3}}{3} + x^{2}
Simplify
The graph
-2.0-1.8-1.6-1.4-1.2-1.0-0.8-0.6-0.4-0.20.02.5-2.5
Plot the graph f(x)
The answer [src] 
4/3
43\frac{4}{3} 
=
= 
4/3
43\frac{4}{3} 
4/3
Numerical answer [src] 
1.33333333333333
1.33333333333333

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

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