- #1
DrummingAtom
- 659
- 2
Homework Statement
Integral of sqrt(1+ln x)/(x*ln x)
Homework Equations
The Attempt at a Solution
I've tried substitutions and they seem to lead to nowhere. I need help getting started on this one. Thanks
DrummingAtom said:Oooppss. I got it now, I had to double substitute.
Apphysicist said:But...why?
u=lnx, du=1/x
thus sqrt(u)du/u= u^(-1/2)du...easy power rule, and that's only one sub...
DrummingAtom said:But where does the 1 go? The answer would then be 2sqrt(ln x) which doesn't equal the original function.
An integral is a mathematical concept that represents the accumulation or total value of a quantity, typically represented as the area under a curve in a graph. It is used to find the exact or approximate value of a function over a given interval.
To solve an integral, you can use various methods such as substitution, integration by parts, or trigonometric substitution. In this case, the integral of sqrt(1+ln x)/(x*ln x) can be solved using integration by parts.
The main purpose of finding an integral is to solve problems involving the accumulation of a quantity over a given interval. It is also used in various fields such as physics, engineering, and economics to calculate important values and make predictions.
The choice of integration technique depends on the form of the integrand. Generally, it is helpful to try different techniques and see which one works best. In this case, integration by parts is a suitable method as the integrand contains a product of two functions.
There are certain integrals that have well-known solutions and can be solved using shortcuts such as integration tables or computer programs. However, most integrals require a combination of techniques and may not have a straightforward solution. Therefore, it is important to have a good understanding of different integration techniques and when to use them.