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int(x^3-4x^2+6x+5)/(x^2-2x+3)dx=...

`int(x^3-4x^2+6x+5)/(x^2-2x+3)dx=`

A

`(x^2)/(2)+2x+(1)/(2)log|x^2-2x+3|+(10)/(sqrt(2))tan^(-1)((x-1)/(sqrt(2)))+c`

B

`(x^2)/(2)+2x+(1)/(2)log|x^2-2x+3|+(5)/(sqrt(2))tan^(-1)((x-1)/(sqrt(2)))+c`

C

`(x^2)/(2)-2x-(1)/(2)log|x^2-2x+3|+(10)/(sqrt(2))tan^(-1)((x-1)/(sqrt(2)))+c`

D

`(x^2)/(2)-2x-(1)/(2)log|x^2-2x+3|+(5)/(sqrt(2))tan^(-1)((x-1)/(sqrt(2)))+c`

Text Solution

Verified by Experts

The correct Answer is:
C
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