When you make a substitution, replace everything. Here you still have a factor of x remaining. If u = ln(x), what is x in terms of u? Also, and this is related, did you replace dx by its appropriate expression involving du?stau40 said:It would be 1/(x(u)^3)
stau40 said:Ok, it should be the antiderivative of du/(u^3) but I still don't understand how to work thru the third power. If I solve for the antiderivative and end up with u^4 I would need (1/4) in front of u and that gets me to the wrong result.
An antiderivative is the inverse operation of a derivative. It is a function that, when differentiated, gives the original function.
Solving antiderivative problems helps us find the original function that was differentiated, which can be useful in a variety of applications such as physics, economics, and engineering.
To find the antiderivative of a function, you can use the reverse power rule, integration by parts, or other integration techniques. It is important to remember to include the constant of integration when solving an antiderivative problem.
Yes, there are some special cases when solving antiderivative problems. For example, some functions may not have an antiderivative that can be expressed in terms of elementary functions, and in these cases, we must use numerical methods to approximate the value of the antiderivative.
Antiderivatives have many practical applications, such as calculating displacement from velocity, finding the area under a curve, and determining the amount of work done by a force. They are also used in fields like economics to model changes in supply and demand.