Question

I need to understand this problem. Integrate 7xcos^4x^2 dx

Answer 1

\[\int\limits_{}^{}7xcos ^{4}x ^{2} dx\]

Answer 2

Allright. First we need to take care of that x^2 inside the cosine.

Answer 3

Do you see how we would do that?

Answer 4

By using a u sub?

Answer 5

Good job :) .

Answer 6

So u=x^2 and du=2x dx

Answer 7

or du/2 = x dx

Answer 8

Recall that 7 is a constant which can be pulled outside the intergal.

Answer 9

So what do you obtain?

Answer 10

After you get it into the `u form` like you had in the last post,
I would finish it up by using the `Cosine Reduction Formula` like we did earlier. :)

If applying double angle over and over works better for you though, you can do that.

Answer 11

okay, awesome. The 7 is part of what was throwing me off. So now we have \[7\int\limits_{}^{} \cos ^{4}(u) \frac{ du }{ 2 }\]

Answer 12

Yep that's what I am doing @zepdrix :P . Just walking him through :) .

Answer 13

her* :P

Answer 14

du/2 is really 1/2 * du . We can also pull out that 1/2 in front of the integral :) .

Answer 15

Sorry X) .

Answer 16

so we CAN use the cosine reduction formula?

Answer 17

Yep :) .

Answer 18

We obtain: