Workout the denominator in the form ∫▒〖1/√(a^2-x^2 ) OR 〗 ∫▒〖1/√(a^2+x^2 ) 〗and then use the formula

∫▒〖1/√(a^2-x^2 ) dx = sin^(-1)〖x/a+C OR 〗 ∫▒〖1/√(a^2+x^2 ) 〗 dx= log〖|x+ 〗 √(a^2+x^2 )|+C〗

2 + 3x – 2x2 = 2 – 2[ x2 - 3/2 x] = 2 – 2[ x2 - 3/2 x + 〖(3/4)〗^2- 〖(3/4)〗^2]

= 2 – 2[ 〖( x- 3/4)〗^2- 〖(3/4)〗^2]

= 2[ 1 – 〖( x- 3/4)〗^2+ 9/16]

= 2[25/16 – 〖( x- 3/4)〗^2]

Etc…