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(x+2)^2dx

Integral of (x+2)^2dx dx

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The solution

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01(x+2)2dx\int\limits_{0}^{1} \left(x + 2\right)^{2}\, dx
Integral((x + 2)^2, (x, 0, 1))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    1. Let u=x+2u = x + 2.

      Then let du=dxdu = dx and substitute dudu:

      u2du\int u^{2}\, du

      1. The integral of unu^{n} is un+1n+1\frac{u^{n + 1}}{n + 1} when n1n \neq -1:

        u2du=u33\int u^{2}\, du = \frac{u^{3}}{3}

      Now substitute uu back in:

      (x+2)33\frac{\left(x + 2\right)^{3}}{3}

    Method #2

    1. Rewrite the integrand:

      (x+2)2=x2+4x+4\left(x + 2\right)^{2} = x^{2} + 4 x + 4

    2. 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:

        4xdx=4xdx\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 n1n \neq -1:

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

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

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

        4dx=4x\int 4\, dx = 4 x

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

  2. Now simplify:

    (x+2)33\frac{\left(x + 2\right)^{3}}{3}

  3. Add the constant of integration:

    (x+2)33+constant\frac{\left(x + 2\right)^{3}}{3}+ \mathrm{constant}


The answer is:

(x+2)33+constant\frac{\left(x + 2\right)^{3}}{3}+ \mathrm{constant}

The answer (Indefinite) [src]
  /                          
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 |        2          (x + 2) 
 | (x + 2)  dx = C + --------
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(x+2)2dx=C+(x+2)33\int \left(x + 2\right)^{2}\, dx = C + \frac{\left(x + 2\right)^{3}}{3}
The graph
0.001.000.100.200.300.400.500.600.700.800.90010
The answer [src]
19/3
193\frac{19}{3}
=
=
19/3
193\frac{19}{3}
19/3
Numerical answer [src]
6.33333333333333
6.33333333333333
The graph
Integral of (x+2)^2dx dx

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