Question

integration of log x

Answer 1

Integral log x= log x.1

Now use formula for product of two functions

= log x.(integral of 1) -[integral of {derivative of log x.(integral of 1)}]

= x.log x-integral of (1/x . x) + c

=x.log x-x+c

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Answer 2

Answer:

Integration of logx is x(logx-1) + c

Explanation:

What is Integration ?

The summing of discrete data is shown by the integration. To determine the functions that will characterise the area, displacement, and volume that result from a combination of tiny data that cannot be measured separately, integrals are computed. The concept of limit is employed broadly in calculus whenever algebra and geometry are applied. Limits aid us in the study of the outcome of points on a graph such as how they move closer to each other until their distance is virtually zero.

Integration by parts is used to integrate the product of two or more functions. The two functions to be integrated f(x) and g(x) are of the form

∫f(x).g(x).

∫logx.dx

= ∫ 1.logx dx  

= logx ∫ 1.dx - $\int (\frac{d}{dx}logx\int\limits {x} \, dx )dx$

= x.logx - ∫$\frac{1}{x} *x \ dx$ + c

= xlogx - ∫1. dx + c

= xlogx -x + c

Integration of logx is x(logx-1) + c

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