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Integrate with respect to x: i) 1/((x+1...

Integrate with respect to x: i) `1/((x+1)sqrt(x+2))`

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i) `ln|(sqrt(x+2)-1)/(sqrt(x+2)+1)|+C`, ii) `1/(4sqrt(3))ln|(t-sqrt(3))/(t+sqrt(3))|-1/2tan^(-1)t+C`, where `t=sqrt(x+1)` , iii) `-1/sqrtln|(t-1/3)+sqrt((t-1/3)^(2)+2/9|+C`, where `t=1/(x+1)`
iv) `-tan^(-1)sqrt(x^(2)+2)/(x^(2))+C` v) `1/sqrt(6)tan^(-1)(sqrt(3)tanx)/(sqrt(2))+C`, vi) `ln|1-cotx|+C`
vii) `tanx+1/4sin2x-(3x)/(2)+C`
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