# Leibniz Integral Rule Explained

• alijan kk
In summary, the problem is to find the derivative of a function, and the student has tried to do it by using the general definition of logarithms.
alijan kk
1. The problem statement, a
ll variables and given/known data

## The Attempt at a Solution

what is t equal to here , how should i think it ?

#### Attachments

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Last edited:
Where have you tried to start? There must be something to give you a hint or clue.

alijan kk
Greg Bernhardt said:
Where have you tried to start? There must be something to give you a hint or clue.
i have been thinking about it ,,, tried many weird tricks ,, can you tell me a little about the variable t a little please..

There is nothing special about ##t##. It is just the variable of integration. What "weird tricks" have you tried? You have to show us what you have tried. What methods do you know to do integrals?
While I am at it, I should mention that it is impolite to start threads then abandon them, as you seem to have a habit of doing.

member 587159, epenguin and alijan kk
LCKurtz said:
There is nothing special about ##t##. It is just the variable of integration. What "weird tricks" have you tried? You have to show us what you have tried. What methods do you know to do integrals?
While I am at it, I should mention that it is impolite to start threads then abandon them, as you seem to have a habit of doing.
oh i am sorry ,, ok i am going to show what i have done

LCKurtz said:
There is nothing special about ##t##. It is just the variable of integration. What "weird tricks" have you tried? You have to show us what you have tried. What methods do you know to do integrals?
While I am at it, I should mention that it is impolite to start threads then abandon them, as you seem to have a habit of doing.
should i post it on "Mathematics" if i don't know how to start ?

For one thing, you haven't given a complete statement of the problem. What are you asked to do with the given formula?

LCKurtz said:
There is nothing special about ##t##. It is just the variable of integration. What "weird tricks" have you tried? You have to show us what you have tried. What methods do you know to do integrals?
While I am at it, I should mention that it is impolite to start threads then abandon them, as you seem to have a habit of doing.
LCKurtz said:
There is nothing special about ##t##. It is just the variable of integration. What "weird tricks" have you tried? You have to show us what you have tried. What methods do you know to do integrals?
While I am at it, I should mention that it is impolite to start threads then abandon them, as you seem to have a habit of doing.
i have uploaded an other image , , and i have to find derivatives,, and i think it is based on the general definition of logarithms

So now you have stated the question and posted the answer. If you are asking how that answer was obtained, look up Leibniz integral rule either online or in your textbook.

alijan kk
LCKurtz said:
So now you have stated the question and posted the answer. If you are asking how that answer was obtained, look up Leibniz integral rule either online or in your textbook.
very helpful, thankyou again <3

## What is logarithmic integration?

Logarithmic integration is a mathematical technique used to integrate functions involving logarithms. It involves using the properties of logarithms to simplify the integral and then using standard integration methods to solve it.

## Why is logarithmic integration useful?

Logarithmic integration is useful in situations where the function being integrated involves logarithms. It allows us to solve integrals that would otherwise be difficult or impossible to solve using other integration techniques.

## What are the steps involved in logarithmic integration?

The steps involved in logarithmic integration are: 1) Simplify the integral using the properties of logarithms, 2) Rewrite the integral using basic integration techniques, such as substitution or integration by parts, and 3) Solve the integral using the resulting formula.

## What are some common applications of logarithmic integration?

Logarithmic integration is commonly used in fields such as physics, engineering, and economics to solve problems involving exponential growth or decay. It is also used in statistics to calculate probabilities and in finance to model compound interest.

## What are the limitations of logarithmic integration?

Logarithmic integration can only be used to solve integrals involving logarithmic functions. It is not applicable to integrals involving other types of functions. Additionally, it can be time-consuming and difficult to use for more complex functions.

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