Evaluate: `int(x-3)sqrt(x^2+3x-18) dx`

1.	Evaluate: `int(x-3)sqrt(x^2+3x-18) dx`
Answer» Correct Answer - `(1)/(3)(x^(2)+3x-18)^(3//2)-(9)/(8){(2x+3)sqrt(x^(2)+3x-18)}-(81)/(2)log\|x+(3)/(2)+sqrt(x^(2)+3x-18)\|+C` Let `(x-3)=A*(d)/(dx)(x^(2)+3x-18)+B`. Then `thereforeI=(1)/(2)int(2x+3)sqrt(x^(2)+3x-18)dx-(9)/(2)intsqrt(x^(2)+3x-18)dx` `=(1)/(2)intsqrt(t)dt-(9)/(2)intsqrt((x+(3)/(2))^(2)-((9)/(2))^(2))dx`.

Discussion

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