Question

integral of ( logx)/x

Answer 1

Question :

Evaluate integral log x/x

Solution :

We have to integrate logx /x

$\sf\int\dfrac{\log\:x}{x}$

Let t = log x

Now Differentiate with respect to x

$\sf\dfrac{dt}{dx}=\dfrac{1}{x}$

$\sf\:xdt=dx...(1)$

Now ,

$\sf\int\dfrac{\log\:x}{x}=\int\dfrac{t}{x}\times\:xdt$

$\sf=\int\:tdt$

We know that

$\rm\int\:x^n=\dfrac{x{}^{n+1}}{n+1}$

$\sf=\dfrac{t^2}{2}+c$

$\sf=\dfrac{(\log\:x)^2}{2}+c$

Answer 2

Answer:

Evaluate the following integral: \[ \ int x \log x \, dx. \]. We use integration by parts, defining. \begin{align*} u &= \log x & du &= Then we ...