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Integrate the following functions 1/sqrt...

Integrate the following functions `1/sqrt((2-x)^2+1)`

Text Solution

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`int 1/(sqrt(2-x)^2+1) dx`
=`1/-1 log|2-x +sqrt((2-x)+1)|+c`
=`-log|2-x+sqrt((2-x)^2+1)|+c`
=`log|2-x+sqrt((4-4x+x^2)+1)|^-1+c`
`log|1/(2-x+sqrt(x^2-4x+5)|+c`
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