glomar said:Homework Statement
I have to solve the following integral
1/(sqrt[x] * ln[x]) from 2 to infinity
Homework Equations
The Attempt at a Solution
u= ln[x] dv=1/sqrt(x)
du= 1/x v= 2 sqrt(x)
If I do this I get
lim (ln b/ sqrt[x] - 4 sqrt[x] - ln2/sqrt[x] + 4 sqrt[x])
Is this the actual result of the integral? Did I substitute correctly?
Thanks in advance!
Integration by parts is typically used when you have a product of two functions in your integral. It can also be used to integrate functions that are the product of a polynomial and an exponential function.
The formula for integration by parts is ∫udv = uv - ∫vdu, where u is the first function and dv is the second function.
There is no one set rule for choosing u and dv, but a common approach is to choose u as the function that becomes simpler when differentiated, and dv as the function that becomes easier to integrate.
If the integral becomes more complicated after using integration by parts, you can try using the formula again on the new integral. If this doesn't work, you may need to try a different integration technique.
No, integration by parts is just one of many integration techniques and it may not always work for every integral. It is important to be familiar with other integration methods as well.