Evaluate the integral

Let us denote the above integral wit 

Use formula for sine of double angle:

Let us denote the above two integrals with  and  respectively.

To calculate  we use sine of double angle formula.

Using the fact that  we can write...

Let us denote the above integral wit 

Use formula for sine of double angle:

Let us denote the above two integrals with  and  respectively.

To calculate  we use sine of double angle formula.

Using the fact that  we can write the above as

Now we use the fact that

Therefore, since  we have

Let us now calculate

Use the following formula:

Now we proceed as we did in calculating We use formula for sine of double angle.

Since  we get

We can now calculate our starting integral 

                                                                                                        

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