Integration problem help

Question

Solve step by step.

 

Answer 1

The integration expression is .

Write the quadratic expression in the complete square form.

= 2+3x-2x².

= -2x²+3x+2.

= -2(x²-3x/2)+2.

= -2(x²-3x/2+9/16-9/16)+2.

= -2(x - 3/4)² + 9/8 + 2.

= -2(x - 3/4)² + 25/8.

= 2[25/16 - (3/4 - x)²].