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If 2x2+5x+9 x2+x+1 dx =x x2+x+1+ x2+x+1 + e |x+ 12+ x2+x+1 |+C, where C is the constant of integration, then +2 is equal to .
16
Differentiate the right side and compare with the integrand; let S= x2+x+1.
ddx(xS)= 4x2+3x+22S, ddx( S)= (2x+1)2S, ddx [ (x+ 12+S ) ]= 2 2S
Sum = 4x2+(3+2 )x+(2+ +2 )2S= 4x2+10x+182S
3+2 =10 = 72
Constants: 2+ +2 =18
+2 =16
Answer: 16
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