f(x) = int (e^(3x)-e^(2x)+x)dx
f(x)= inte^(3x)dx - inte^(2x)dx + intxdx
f(x)=1/3e^(3x)-1/2e^(2x)+1/2x^2 + C ; where C\equivconstant
f(x)=1/3e^(3x)+1/2 (x^2-e^(2x)) + C
f(0) = 1/3e^(3(0))-1/2e^(2(0))+cancel(1/2(0)^2) + C = -2
1/3e^(0)-1/2e^(0)+ C = -2
1/3(1)-1/2(1)+ C = -2
1/3 - 1/2 + C = -2
2/6 - 3/6 + C = -12/6
- 1/6 + C = -12/6
C = -11/6
Hence:
f(x)=1/3e^(3x)+1/2 (x^2-e^(2x)) -11/6