What is $int (-2x^3-x^2+x+2 ) / (3x^2+2x +3 )$ ?

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Answer 1 · 2017-12-17T18:26:20

$(25Ln(3x^2+2x+3)+10sqrt2arctan((3x+1)/(2sqrt2))-18x^2+6x)/54+C$ or

= $25/54Ln(3x^2+2x+3)+(5sqrt2)/27arctan((3x+1)/(2sqrt2))-(3x^2-x)/9+C$

$int (-2x^3-x^2+x+2)/(3x^2+2x+3)*dx$

= $-1/9int (18x^3+9x^2-9x-18)/(3x^2+2x+3)*dx$

= $-1/9int ((6x-1)*(3x^2+2x+3)-(25x+15))/(3x^2+2x+3)*dx$

= $-1/9int (6x-1)dx$ + $1/9int (25x+15)/(3x^2+2x+3)*dx$

= $-1/9*(3x^2-x)+C$ + $1/9int (25/6*(6x+2)+20/3)/(3x^2+2x+3)*dx$

= $-1/9*(3x^2-x)+C$ + $25/54int (6x+2)/(3x^2+2x+3)*dx$ + $20/27int (dx)/(3x^2+2x+3)$

= $-1/9*(3x^2-x)+25/54ln(3x^2+2x+3)+C$ + $20/27int (3dx)/(9x^2+6x+9)$

= $-1/9*(3x^2-x)+25/54ln(3x^2+2x+3)+C$ + $20/27int (3dx)/((3x+1)^2+(2sqrt2)^2)$

= $-1/9*(3x^2-x)+25/54ln(3x^2+2x+3)$ + $(5sqrt2)/27arctan((3x+1)/(2sqrt2))+C$

= $(25Ln(3x^2+2x+3)+10sqrt2arctan((3x+1)/(2sqrt2))-18x^2+6x)/54+C$

What is int (-2x^3-x^2+x+2 ) / (3x^2+2x +3 )int (-2x^3-x^2+x+2 ) / (3x^2+2x +3 )?