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(2x+1)^3

Integral of (2x+1)^3 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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 |           3   
 |  (2*x + 1)  dx
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$$\int\limits_{0}^{1} \left(2 x + 1\right)^{3}\, dx$$
Integral((2*x + 1)^3, (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 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]
  /                              
 |                              4
 |          3          (2*x + 1) 
 | (2*x + 1)  dx = C + ----------
 |                         8     
/                                
$$2\,x^4+4\,x^3+3\,x^2+x$$
The graph
The answer [src]
10
$$10$$
=
=
10
$$10$$
Numerical answer [src]
10.0
10.0
The graph
Integral of (2x+1)^3 dx

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