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Integral of (x+5)^2 dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
  8            
  /            
 |             
 |         2   
 |  (x + 5)  dx
 |             
/              
4              
$$\int\limits_{4}^{8} \left(x + 5\right)^{2}\, dx$$
Integral((x + 5)^2, (x, 4, 8))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    1. Let .

      Then let and substitute :

      1. The integral of is when :

      Now substitute back in:

    Method #2

    1. Rewrite the integrand:

    2. Integrate term-by-term:

      1. The integral of is when :

      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          (x + 5) 
 | (x + 5)  dx = C + --------
 |                      3    
/                            
$$\int \left(x + 5\right)^{2}\, dx = C + \frac{\left(x + 5\right)^{3}}{3}$$
The graph
The answer [src]
1468/3
$$\frac{1468}{3}$$
=
=
1468/3
$$\frac{1468}{3}$$
1468/3
Numerical answer [src]
489.333333333333
489.333333333333

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