U-Substitution problem

Hi guys! I'm doing my Calc homework right now and am having a little trouble with some problems. I did one but I'm not really sure if i did it right. Could you check for me?

∫Sin^5(2x)Cos(2x)

U= Sin(2x)
Du/Dx= Cos(2x)/2
Dx= du/2cos(2x)

(U)^5 Cos(2x) Du/Cos(2x)/2

So the Cos(2x) cancels and I’m left with

½ (U)^5

Now I have to do the anti derivative

1/12U^6

1/2Sin^6(2x)

Is that right? If not, what did I do wrong?

Quote:

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Originally Posted by gocubs526

Hi guys! I'm doing my Calc homework right now and am having a little trouble with some problems. I did one but I'm not really sure if i did it right. Could you check for me?

∫Sin^5(2x)Cos(2x)

U= Sin(2x)
Du/Dx= Cos(2x)/2
Dx= du/2cos(2x)

(U)^5 Cos(2x) Du/Cos(2x)/2

So the Cos(2x) cancels and I’m left with

½ (U)^5

Now I have to do the anti derivative

1/12(U^6)

1/2Sin^6(2x) ?

I think you mean

Is that right? If not, what did I do wrong?

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remember that you can always check your antiderivative by taking the derivative of your solution.

your answer is correct.