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Integral of (x+2)^4 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 -2            
  /            
 |             
 |         4   
 |  (x + 2)  dx
 |             
/              
-1             
$$\int\limits_{-1}^{-2} \left(x + 2\right)^{4}\, dx$$
Integral((x + 2)^4, (x, -1, -2))
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 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]
  /                          
 |                          5
 |        4          (x + 2) 
 | (x + 2)  dx = C + --------
 |                      5    
/                            
$$\int \left(x + 2\right)^{4}\, dx = C + \frac{\left(x + 2\right)^{5}}{5}$$
The graph
The answer [src]
-1/5
$$- \frac{1}{5}$$
=
=
-1/5
$$- \frac{1}{5}$$
-1/5
Numerical answer [src]
-0.2
-0.2

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