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Evaluate: (i) int1/(4x^2+4x+5)\ dx...

Evaluate: (i) `int1/(4x^2+4x+5)\ dx`

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`text { Let I }=int frac{d x}{4 x^{2}+4 x+1+4} `
`=int frac{d x}{(2 x)^{2}+2 times 2 x+1+22} `
`=int frac{d x}{(2 x+1)^{2}+2^{2}} `
`text { Putting }(2 x+1)=t `
`Rightarrow 2 dx=dt `
`Rightarrow d x=frac{d t}{2} `
`therefore I=frac{1}{2} int frac{d t}{t^{2}+2^{2}} `
`=frac{1}{2} times frac{1}{2} tan ^{-1}(frac{t}{2})+C `
...
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