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Evaluate: (i) int1/(4x^2-4x+3)\ dx (ii) ...

Evaluate: (i) `int1/(4x^2-4x+3)\ dx` (ii) `int1/(x^2+4x+8)\ ` (iii) `int1/(9x^2+6x+10)`

Text Solution

Verified by Experts

`int (1)/(4x^(2)+4x+5)dx=1/4int(1)/(x^(2)+x+(5)/(4))dx`
`=1/4int(1)/((x^(2)+x+1/4)+1)dx =1/4 int(1)/((x+1/2)^(2)+1^(2))dx`
`=1/4 tan^(-1) ((x+(1)/(2))/(1)) +c=1/4tan^(-1) ((2x+1)/(2)) +c.`
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