How to solve for the integral of sin(3x) times x using integration by parts?

[FARADAY JR]

Homework Statement

I have work these two problems, but in the first one #4 I feel like I'm missing something a step or something. and in the second problem I'm just lost, I can't finish it so will you please assist me. your help is appreciated.

Homework Equations

thanks a lot.

The Attempt at a Solution

 

[King Tony]

You got the first question right except I think you just mis-wrote your final answer that's boxed. It looks like you accidentally moved the x^6 to the bottom when you went to the last step.

 

[Mark44]

How about posting the 2nd problem so that we don't have to turn our heads sideway to read it?

 

[dextercioby]

For the integral from the second picture you need to apply 2ice the partial integration.

 

[FARADAY JR]

You got the first question right except I think you just mis-wrote your final answer that's boxed. It looks like you accidentally moved the x^6 to the bottom when you went to the last step.

do you mean the X^6 that comes after the (1/36)

 

[FARADAY JR]

How about posting the 2nd problem so that we don't have to turn our heads sideway to read it?

ok, I need to know how to proceed with the second integration

 

[Mark44]

ok, I need to know how to proceed with the second integration

Repost the second problem then. I don't want to have to turn my monitor sideways to read your work.

 

[FARADAY JR]

Repost the second problem then. I don't want to have to turn my monitor sideways to read your work.

I uploaded it agin, but it's not rotating I don't know why

 

[Bohrok]

Side note: some graphics cards let you rotate your monitor display in its settings. If you happen to have an Intel graphics card on your computer, holding Ctrl and Alt while hitting the left arrow key will rotate the screen and make the image readable, then hold Ctrl and Alt and hit the up arrow to put it back to normal.

 

[FARADAY JR]

side note: Some graphics cards let you rotate your monitor display in its settings. If you happen to have an intel graphics card on your computer, holding ctrl and alt while hitting the left arrow key will rotate the screen and make the image readable, then hold ctrl and alt and hit the up arrow to put it back to normal.

thank you so much

 

[SammyS]

For the integral:

$$\int\sin(3x)\,x\,dx\,,$$

let $$u=x$$ and $$dv=\sin(3x)\,dx\,.$$