Evaluate: `int1/(sqrt(3x^2+5x+7))\ dx`

Explanation

I=`int1/(sqrt(3x^2+5x+7))\ dx`

`I=1/(sqrt3)int1/(sqrt(x^2+5/3x+7/3))\ dx`

`I=1/(sqrt3)int1/(sqrt((x+5/6)^2+(59)/(36))\ dx`

let `(x+5/6)=t`

so,

`dx=dt`

Thus,

`I=1/(sqrt3)int1/(sqrt(t^2+(59)/(36))\ dx`

...