Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) cos(x) sin(2x) sin(x) dx

Step-by-step explanation:

Given

Required

Evaluate

Rewrite as:

In trigonometry:

Divide both sides by 2

Substitute for

Let

Differentiate:

Make the subject

Substitute for

Substitute 2x for u

At this point, we apply the reduction formula:

Which is:

Let n = 2; So, we have:

So, we have:

Integrate 1 with respect to u

Recall that:

So, we have:

Open bracket

Recall that:   and        

So, the expression becomes:

Add constant c

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In trigonometry:

Divide both sides by 2

Replace 2x with

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becomes

The solution can be further simplified as: