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Evaluate: (i) int1/(4x^2+12 x+5)\ dx (ii...

Evaluate: (i) `int1/(4x^2+12 x+5)\ dx` (ii) `int1/(x^2-10 x+34)\ dx`

Text Solution

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y=`int1/(4x^2+12 x+5)\ dx`
=`1/4int 1/(x^2+3 x+5/4)\ dx`
=`1/4int 1/(x^2+2x.(3/2) +(3/2)^2-(3/2)^2+5/4)\ dx`
=`1/4int dx/((x+3/2)^2-1)`
Let` (x+3/2)=t`
`dx=dt`
...
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