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x^2+3x+2

Integral of x^2+3x+2 dx

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The solution

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01((x2+3x)+2)dx\int\limits_{0}^{1} \left(\left(x^{2} + 3 x\right) + 2\right)\, dx
Integral(x^2 + 3*x + 2, (x, 0, 1))
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 n1n \neq -1:

        x2dx=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:

        3xdx=3xdx\int 3 x\, dx = 3 \int x\, dx

        1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n1n \neq -1:

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

        So, the result is: 3x22\frac{3 x^{2}}{2}

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

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

      2dx=2x\int 2\, dx = 2 x

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

  2. Now simplify:

    x(2x2+9x+12)6\frac{x \left(2 x^{2} + 9 x + 12\right)}{6}

  3. Add the constant of integration:

    x(2x2+9x+12)6+constant\frac{x \left(2 x^{2} + 9 x + 12\right)}{6}+ \mathrm{constant}


The answer is:

x(2x2+9x+12)6+constant\frac{x \left(2 x^{2} + 9 x + 12\right)}{6}+ \mathrm{constant}

The answer (Indefinite) [src]
  /                                       
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 | \x  + 3*x + 2/ dx = C + 2*x + -- + ----
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((x2+3x)+2)dx=C+x33+3x22+2x\int \left(\left(x^{2} + 3 x\right) + 2\right)\, dx = C + \frac{x^{3}}{3} + \frac{3 x^{2}}{2} + 2 x
The graph
0.001.000.100.200.300.400.500.600.700.800.90010
The answer [src]
23/6
236\frac{23}{6}
=
=
23/6
236\frac{23}{6}
23/6
Numerical answer [src]
3.83333333333333
3.83333333333333
The graph
Integral of x^2+3x+2 dx

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