Easy integration by parts help

In summary, when trying to integrate ln(2x+1), you can choose to substitute 2x+1 with p first and then use integration by parts, or you can directly use ln(2x+1) as u and 1 as dv/dx. Both methods will result in the same answer, but substituting first is simpler.
  • #1
MillerGenuine
64
0

Homework Statement



integral of ln(2x +1)

Homework Equations


I know this is an easy problem but i can not seem to figure out what to substitute for my U and my dV. I was thinking on making my U= 2x+ 1. but then my problem is what would my dV be? ln U? lnx? the ln is throwing me off a bit. I am not sure what it is the ln of.


The Attempt at a Solution



U= 2x+1 dV= lnU (?)
dU/2= dx V= 1/U (?)
 
Physics news on Phys.org
  • #2
When you want to integrate by parts, a good choice for u is that part which has a simple derivative, and for v that part which is easy to integrate. So you can choose ln(2x+1)=u and 1=dv/dx

ehild
 
  • #3
ok perfect. got the answer. I have seen it done the way you just showed & i have also seen it done a different way. If we first substitute
p= 2x+1
dp/2 = dx
then once this is done we have 2 integral ln(p).
now from here we do integration by parts by choosing
u= ln(p) dV= dp
du= 1/p V= p

now is there any difference between the two? or any situations where one will work and the other wont?
 
  • #4
Both methods have the same result, but substituting first 2x+1 by p is much simpler. Do not forget to plug in 2x+1 for p at the end.

ehild
 

FAQ: Easy integration by parts help

What is integration by parts?

Integration by parts is a calculus technique that allows us to find the integral of a product of two functions by transforming it into a simpler form.

Why is it important to learn integration by parts?

Integration by parts is an important tool in solving many types of integrals, especially those involving products of functions. It is also useful for finding antiderivatives and evaluating definite integrals.

How do you determine which function to integrate and which to differentiate?

The general rule is to choose the function that becomes simpler when differentiated and the other function to integrate. This is commonly known as the "LIATE" rule, where L stands for logarithmic, I for inverse trigonometric, A for algebraic, T for trigonometric, and E for exponential functions.

What are the steps for using integration by parts?

The steps for using integration by parts are as follows: 1) Identify the function to integrate and the function to differentiate. 2) Apply the integration by parts formula: ∫udv = uv - ∫vdu. 3) Evaluate the integral of the differentiated function using integration techniques. 4) Substitute the values of u and v back into the formula to get the final answer.

Can integration by parts be used to solve all types of integrals?

No, integration by parts can only be used for certain types of integrals, particularly those that involve products of functions. Other integration techniques, such as substitution and partial fractions, may be required for different types of integrals.

Similar threads

Replies
22
Views
2K
Replies
15
Views
1K
Replies
1
Views
1K
Replies
14
Views
1K
Replies
21
Views
2K
Replies
3
Views
1K
Replies
1
Views
1K
Back
Top