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Integral of (2x+3)^2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  0              
  /              
 |               
 |           2   
 |  (2*x + 3)  dx
 |               
/                
2                
$$\int\limits_{2}^{0} \left(2 x + 3\right)^{2}\, dx$$
Integral((2*x + 3)^2, (x, 2, 0))
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          (2*x + 3) 
 | (2*x + 3)  dx = C + ----------
 |                         6     
/                                
$$\int \left(2 x + 3\right)^{2}\, dx = C + \frac{\left(2 x + 3\right)^{3}}{6}$$
The graph
The answer [src]
-158/3
$$- \frac{158}{3}$$
=
=
-158/3
$$- \frac{158}{3}$$
-158/3
Numerical answer [src]
-52.6666666666667
-52.6666666666667

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