Difficulty With Integration by Parts

In summary, the conversation discusses finding the derivative of u in an integral with respect to y. It is suggested to use the u-substitution method and treat x as a variable and y as a constant. Another approach is to use a w substitution to simplify the integration by parts.
  • #1
Shoney45
68
0

Homework Statement


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Homework Equations





The Attempt at a Solution

What I am unsure of is how to find the derivative of u. Since the original integral is integrating with respect to y, should I be finding the derivative of u with respect to y, and treat the x's as contants?
 
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  • #2
I think it's possible to solve it in terms of x

let u=x and dv=e^(-x(1+y))

then,
du=1
and v= [e^(-x(1+y))]/(-(1+y))

I think it should work

if you want let
u=e^(-x(1+y))

du= -(1+y)*e^(-x(1+y))

you treat y as a constant and x as a variable
(I am assuming you want to integrate in terms of x)
 
  • #3
Alrighty then - I'll get to work. Thanks for the direction.
 
  • #4
Roni1985 said:
I think it's possible to solve it in terms of x

let u=x and dv=e^(-x(1+y))

then,
du=1
and v= [e^(-x(1+y))]/(-(1+y))

Actually du = dx, also dv=e^(-x(1+y))dx

You can simplify this problem, by performing a w substitution at the beginning ie. consider w = -x*(1+y). It will make the integration by parts less of a headache.
 

1. What is integration by parts?

Integration by parts is a method of integration used to evaluate the integral of a product of two functions. It involves breaking down the original integral into smaller, more manageable parts and using a specific formula to solve for the final answer.

2. Why is integration by parts difficult?

Integration by parts can be difficult because it requires a good understanding of integration and the ability to recognize which parts of the integral should be designated as u and dv. It also involves multiple steps and can be time-consuming.

3. How do I know when to use integration by parts?

Integration by parts is typically used when the integral involves a product of two functions, one of which can be easily integrated while the other cannot. This method is also useful when the integral involves a power of x or an exponential function.

4. What are some tips for solving integration by parts?

Some tips for solving integration by parts include choosing u and dv carefully, using the LIATE rule (choose u in the following order: logarithmic, inverse trigonometric, algebraic, trigonometric, exponential), and being aware of common patterns and substitutions that may simplify the integral.

5. Are there any common mistakes to avoid when using integration by parts?

Yes, some common mistakes to avoid when using integration by parts include forgetting to differentiate u, integrating dv incorrectly, and not simplifying the final answer. It is also important to check for any algebraic errors and to double check the final answer with differentiation.

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