- #1

- 186

- 2

I got:

4[1/4xe^(4x)-1/16e^(4x)+c] ?

which reduces to

xe^(4x)-1/4e^(4x)+c

Is this the correct integral?

Thanks.

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter lonewolf219
- Start date

In summary, integration by parts with e involves differentiating the solution and checking if it matches the original integrand. The formula for this method is ∫ u dv = uv - ∫ v du, where u and v are functions and dv and du are their respective differentials. When choosing which function to use as u and which as dv, the acronym LIPET (Logarithmic, Inverse trigonometric, Polynomial, Exponential, Trigonometric) can be helpful. However, integration by parts with e is not suitable for all types of integrals and there are other methods such as substitution, partial fractions, and trigonometric substitutions. It is important to be familiar with multiple methods as different integrals may require different

- #1

- 186

- 2

I got:

4[1/4xe^(4x)-1/16e^(4x)+c] ?

which reduces to

xe^(4x)-1/4e^(4x)+c

Is this the correct integral?

Thanks.

Physics news on Phys.org

- #2

Homework Helper

- 2,461

- 158

check by differentiating

- #3

- 186

- 2

I am so glad physics forums exists!

Wow. Of course!

Wow. Of course!

To check the solution to integration by parts with e, you need to differentiate the solution and see if it matches the original integrand. This is because integration by parts is a method of integration that involves the product rule of differentiation.

The formula for integration by parts with e is ∫ u dv = uv - ∫ v du, where u and v are functions and dv and du are their respective differentials.

When choosing which function to use as u and which as dv, it is recommended to follow the acronym LIPET, which stands for Logarithmic, Inverse trigonometric, Polynomial, Exponential, and Trigonometric. The function that falls first in this order should be used as u.

No, integration by parts with e is not suitable for all types of integrals. It is most useful for integrals involving products of functions.

Yes, there are many other methods of integration, such as substitution, partial fractions, and trigonometric substitutions. It is important to understand and be familiar with multiple methods as different integrals may require different approaches.

- Replies
- 2

- Views
- 746

- Replies
- 4

- Views
- 681

- Replies
- 2

- Views
- 1K

- Replies
- 2

- Views
- 1K

- Replies
- 1

- Views
- 1K

- Replies
- 4

- Views
- 1K

- Replies
- 7

- Views
- 580

- Replies
- 6

- Views
- 3K

- Replies
- 21

- Views
- 588

- Replies
- 2

- Views
- 61

Share: