Mathematics

# $\displaystyle \int \dfrac{1}{(x + 1)\sqrt{x + 2}}dx =$

##### SOLUTION
Let, $I=$$\displaystyle \int \dfrac{1}{(x + 1)\sqrt{x + 2}}dx Put x+2=z^2 then dx=2z\ dz. Using these in the above integration we get, I=$$\displaystyle \int \dfrac{2z\ dz}{(z^2 - 1)z}dx$
or, $I=$$2\displaystyle \int \dfrac{ dz}{(z^2 - 1)}dx or, I=$$2.\dfrac{1}{2.1}\log\left|\dfrac{z-1}{z+1}\right|+c$ [ Where $c$ integrating constant]
or, $I=$$\log\left|\dfrac{\sqrt{x+2}-1}{\sqrt{x+2}+1}\right|+c$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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