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Q10  Integrate the functions \frac{1 }{ \sqrt { x ^ 2 + 2 x + 2 }}

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\frac{1 }{ \sqrt { x ^ 2 + 2 x + 2 }} 
the above equation can be also written as, 
=\int\frac{1}{\sqrt{(1+x)^2+1^2}}dx
let 1+x = t
then dx = dt 
therefore,

\\=\int\frac{1}{\sqrt{t^2+1^2}}dx\\ =\log\left | t+\sqrt{t^2+1} \right |+C\\ =\log\left | (1+x)+\sqrt{(1+x)^2+1} \right |+C\\ =\log\left | (1+x)+\sqrt{(x^2+2x+2} \right |+C

Posted by

manish

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