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(8x-12)(4x^2-12x)^4

Integral (8x-12)(4x^2-12x)^4 dx

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  1                             
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 |  (8*x - 12)*\4*x  - 12*x/  dx
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$$\int\limits_{0}^{1} \left(8 x - 12\right) \left(4 x^{2} - 12 x\right)^{4}\, dx$$
Integral((8*x - 12)*(4*x^2 - 12*x)^4, (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 is when :

      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 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:

      The result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The graph
The answer [src]
-32768/5
$$- \frac{32768}{5}$$
=
=
-32768/5
$$- \frac{32768}{5}$$
-32768/5
Numerical answer [src]
-6553.6
-6553.6
The answer (Indefinite) [src]
  /                                                 
 |                                                 5
 |                         4          /   2       \ 
 |            /   2       \           \4*x  - 12*x/ 
 | (8*x - 12)*\4*x  - 12*x/  dx = C + --------------
 |                                          5       
/                                                   
$$\int \left(8 x - 12\right) \left(4 x^{2} - 12 x\right)^{4}\, dx = C + \frac{\left(4 x^{2} - 12 x\right)^{5}}{5}$$

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

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