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x^2+6x+8
Solving integrals/ x^2+6x+8

Integral of x^2+6x+8 dx

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The solution

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∫28(x2+6x+8) dx\int\limits_{2}^{8} \left(x^{2} + 6 x + 8\right)\, dx 
Integral(x^2 + 6*x + 8, (x, 2, 8))
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:

      ∫6x dx=6∫x dx\int 6 x\, dx = 6 \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: 3x23 x^{2}

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

      ∫8 dx=8x\int 8\, dx = 8 x

    The result is: x33+3x2+8x\frac{x^{3}}{3} + 3 x^{2} + 8 x

  2. Now simplify:

    x(x2+9x+24)3\frac{x \left(x^{2} + 9 x + 24\right)}{3}

  3. Add the constant of integration:

    x(x2+9x+24)3+constant\frac{x \left(x^{2} + 9 x + 24\right)}{3}+ \mathrm{constant}

The answer is:

x(x2+9x+24)3+constant\frac{x \left(x^{2} + 9 x + 24\right)}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | \x  + 6*x + 8/ dx = C + 3*x  + 8*x + --
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∫(x2+6x+8) dx=C+x33+3x2+8x\int \left(x^{2} + 6 x + 8\right)\, dx = C + \frac{x^{3}}{3} + 3 x^{2} + 8 x
Simplify
The graph
2.08.02.53.03.54.04.55.05.56.06.57.07.50500
Plot the graph f(x)
The answer [src] 
396
396396 
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396
396396
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Numerical answer [src] 
396.0
396.0
The graph
Integral of x^2+6x+8 dx

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

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