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x^2+4x+3
Solving integrals/ x^2+4x+3

Integral of x^2+4x+3 dx

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The solution

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∫01((x2+4x)+3) dx\int\limits_{0}^{1} \left(\left(x^{2} + 4 x\right) + 3\right)\, dx 
Integral(x^2 + 4*x + 3, (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:

        ∫4x dx=4∫x dx\int 4 x\, dx = 4 \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: 2x22 x^{2}

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

  2. Now simplify:

    x(x2+6x+9)3\frac{x \left(x^{2} + 6 x + 9\right)}{3}

  3. Add the constant of integration:

    x(x2+6x+9)3+constant\frac{x \left(x^{2} + 6 x + 9\right)}{3}+ \mathrm{constant}

The answer is:

x(x2+6x+9)3+constant\frac{x \left(x^{2} + 6 x + 9\right)}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | \x  + 4*x + 3/ dx = C + 2*x  + 3*x + --
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∫((x2+4x)+3) dx=C+x33+2x2+3x\int \left(\left(x^{2} + 4 x\right) + 3\right)\, dx = C + \frac{x^{3}}{3} + 2 x^{2} + 3 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+4x+3 dx

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

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