Mister Exam

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

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### The solution

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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:

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