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• #### How to use it?

• Integral:
• sin^4xcos^4x
• sin⁵x
• cos(x)*dx/(3*x^2+3*sqrt(x))
• cot2x
• #### Identical expressions

• (8x- twelve)(four x^ two -12x)^4
• (8x minus 12)(4x squared minus 12x) to the power of 4
• (8x minus twelve)(four x to the power of two minus 12x) to the power of 4
• (8x-12)(4x2-12x)4
• (8x-12)(4x²-12x)⁴
• (8x-12)(4x to the power of 2-12x) to the power of 4
• (8x-12)(4x^2-12x)^4dx
• #### Similar expressions

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

from to

from to

### The solution

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

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

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