Checking solution to integration by parts with e

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
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Hi, I'm wondering how to integrate 4xe^(4x).


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.
 
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  • #2
check by differentiating
 
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I am so glad physics forums exists!
Wow. Of course!
 

1. How do you check the solution to integration by parts with e?

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.

2. What is the formula for integration by parts with e?

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.

3. How do you choose which function to use as u and which as dv in integration by parts with e?

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.

4. Can integration by parts with e be used for all types of integrals?

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

5. Are there any other methods of integration besides integration by parts with e?

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.

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