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x^2+2x+4
Solving integrals/ x^2+2x+4

Integral of x^2+2x+4 dx

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The solution

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∫01((x2+2x)+4) dx\int\limits_{0}^{1} \left(\left(x^{2} + 2 x\right) + 4\right)\, dx 
Integral(x^2 + 2*x + 4, (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 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}

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

      ∫4 dx=4x\int 4\, dx = 4 x

    The result is: x33+x2+4x\frac{x^{3}}{3} + x^{2} + 4 x

  2. Now simplify:

    x(x2+3x+12)3\frac{x \left(x^{2} + 3 x + 12\right)}{3}

  3. Add the constant of integration:

    x(x2+3x+12)3+constant\frac{x \left(x^{2} + 3 x + 12\right)}{3}+ \mathrm{constant}

The answer is:

x(x2+3x+12)3+constant\frac{x \left(x^{2} + 3 x + 12\right)}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | \x  + 2*x + 4/ dx = C + x  + 4*x + --
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∫((x2+2x)+4) dx=C+x33+x2+4x\int \left(\left(x^{2} + 2 x\right) + 4\right)\, dx = C + \frac{x^{3}}{3} + x^{2} + 4 x
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90010
Plot the graph f(x)
The answer [src] 
16/3
163\frac{16}{3} 
=
= 
16/3
163\frac{16}{3} 
16/3
Numerical answer [src] 
5.33333333333333
5.33333333333333
The graph
Integral of x^2+2x+4 dx

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

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