# Integrating by parts #1

In summary: Then,\frac{du}{dv}=\frac{x}{3}=-\frac{1}{3}=-1.And finally,\frac{du}{dv}=0.thank you so muchYou're welcome.

## 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.

thanks a lot.

## The Attempt at a Solution

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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.

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

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

King Tony said:
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)

Mark44 said:
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

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.

Mark44 said:
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

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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.

bohrok said:

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

For the integral:

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

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

## What is "integrating by parts"?

Integrating by parts is a method used in calculus to solve integrals that involve products of functions.

## When do I use "integrating by parts"?

Integrating by parts is used when the integral involves a product of two functions, and the integral cannot be easily solved by other methods such as substitution or partial fractions.

## How do I use the "integrating by parts" formula?

The formula for integrating by parts is ∫u dv = uv - ∫v du. You must select a function u and its differential du, and another function v and its integral dv, before plugging them into the formula.

## What is the benefit of using "integrating by parts"?

The benefit of using integrating by parts is that it allows for the integration of more complicated functions, especially those that involve products of functions.

## Are there any limitations to using "integrating by parts"?

Integrating by parts may not always result in an integral that can be easily solved. In some cases, it may require multiple applications of the formula or other integration techniques in combination.