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**genlovesmusic09** y= lnx/ 1+lnx find the derivative

use the quotient rule.

integrate from 0 to pie over 2 tan (x/2) dx

let $\displaystyle \textcolor{red}{u = \frac{x}{2}} $

$\displaystyle \textcolor{red}{dx = 2 \, du}$

$\displaystyle \textcolor{red}{2\int_0^{\frac{\pi}{4}} \frac{\sin{u}}{\cos{u}} \, du}$

integrate from pie over 2 to pie 2 cot x/3 dx

same method as above ... let $\displaystyle \textcolor{red}{u = \frac{x}{3}}$

integrate dx/(2 sqaure root of x)(2x)

note that $\displaystyle \textcolor{red}{2\sqrt{x} \cdot 2x = 4x^{\frac{3}{2}}}$