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(3x+2)^2

Integral of (3x+2)^2 dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

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  1              
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 |           2   
 |  (3*x + 2)  dx
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$$\int\limits_{0}^{1} \left(3 x + 2\right)^{2}\, dx$$
Integral((3*x + 2)^2, (x, 0, 1))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    1. Let .

      Then let and substitute :

      1. The integral of a constant times a function is the constant times the integral of the function:

        1. The integral of is when :

        So, the result is:

      Now substitute back in:

    Method #2

    1. Rewrite the integrand:

    2. Integrate term-by-term:

      1. The integral of a constant times a function is the constant times the integral of the function:

        1. The integral of is when :

        So, the result is:

      1. The integral of a constant times a function is the constant times the integral of the function:

        1. The integral of is when :

        So, the result is:

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

      The result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                              
 |                              3
 |          2          (3*x + 2) 
 | (3*x + 2)  dx = C + ----------
 |                         9     
/                                
$$\int \left(3 x + 2\right)^{2}\, dx = C + \frac{\left(3 x + 2\right)^{3}}{9}$$
The graph
The answer [src]
13
$$13$$
=
=
13
$$13$$
13
Numerical answer [src]
13.0
13.0
The graph
Integral of (3x+2)^2 dx

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