These few questions have been bugging me for hours, help would be appreciated
so, dividing both sides by , . Because of that the substitution changes to . Generally speaking, any time you have a square root of a quadratic, you should consider a trig substitution. (Some people prefer hyperbolic functions which satisfy similar identities.)
As for your new question, first complete the square: .
Now the substitution x= t+ 1/3 changes to integrand to