Mathematics

$$\int \dfrac{1}{x\sqrt{1+\ln x}} dx=m\sqrt{(1+\ln x)}+c$$.Find $$m$$


ANSWER

2


SOLUTION

$$\\1+lnx=t^2\\(\frac{1}{x})dx=2tdt\\\therefore I=\int (\frac{2tdt}{\sqrt{t^2}})\\=2\int dt=2t+C\\=2\sqrt{1+lnx}+C\\\therefore\>m=2$$

 

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