Mathematics is an intriguing subject that can be both challenging and rewarding. However, with a solid understanding of its fundamentals, it can become easier to grasp. One of the basic formulas that is frequently used in logarithmic problems is the integration of log x. Integration is simply the process of finding the integral of a function, which provides the area under the curve of the function. With this knowledge, you will be able to approach mathematical problems with confidence and ease.
In this article we would like you to explain in detail about the Integration of log x and its easiest method to know the result. The Integration can be done by using the integration by parts which is also referred to as UV formula.
Integration of Log X
The Integration of log x is the given area under the function of X which is referred as f(x). Below is the mathematical formula for Integration of log x.
Integration of log x = Log X-x+C
Here the x is the variable used and the C is the integration constant.
The logarithmic function is the inverse of the exponential function which is written as Loga x, here is as is the base and x is the index value. The integration symbol which used to describe the Integration of log x will be also referred to when the Integral by Parts methods is used.
The Integration Log x formulae is ∫ln x dx = xlnx – x + C, which is also written as ∫log x dx = log x – x + C
The base of a value if 10, then this formula is being used and for any other value of Base a the respective value will be added in the suffix of log.
Also Read: Derivative of Log X
What is the Integration of Log x with base 10?
The formulae for integration of log x with base 10 can be written as log10x= (logex\ loge10), therefore the integral of log x with base 10 will be x log10x –x / log10x +k, where k is constant.
What is the integration of log 2x?
To find the integration of log 2x, the same formula of the integration by parts to be used where the base can be assumed as null, as it has to be mentioned. x log10x –x / log10x +k the formulae can be written as 2 log 2x-4x+C, where c is the integration constant.
What is the integration of Log Z?
The x log10x –x / log10x +k, can be written with the Logz integration as log(z) the function of Log Z is equal to zlog(z)-z.