Evaluate: (i) `intsqrt(4x^2+9)\ dx` (ii) `intsqrt(x^2+2x+5)\ dx`

Explanation

`int sqrt(4x^(2)+9dx) " ""Let" 2x =t`
` =int sqrt((2x)^(2) +3^(2)) dx rArr 2=(dt)/(dx)`
` =int sqrt(t^(2) +3^(2)).(dt)/(2) rArr dx= (dt)/(2)`
`=1/2 [(t)/(2)sqrt(t^(2)+3^(2)) +(3^(2))/(2) log |t+sqrt(t^(2)+3^(2))|]+c`
` =1/4 [2x sqrt(4x^(2)+9)+9log |2x +sqrt(4x^(2) +9) |]+c`