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∫〖(〖2x〗^3+x^2)/x^2  dx=Ax^2-Bx+c〗;(A+B)^2=

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user3406934 | eNotes Newbie

Posted July 17, 2013 at 7:37 PM via web

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∫〖(〖2x〗^3+x^2)/x^2  dx=Ax^2-Bx+c〗;(A+B)^2=

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted July 17, 2013 at 11:32 PM (Answer #1)

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`int(2x^3+x^2)/x^2dx`

`= int((2x^3)/x^2+x^2/x^2)dx`

`= int(x+1)dx`

`= x^2/2+x+c` where c is a constant.

 

If we comapre the solution with `Ax^2-Bx+c` ;

`Ax^2-Bx+c = x^2/2+x+c`

 

`A = 1/2`

`B = -1`

 

Then;

`(A+B)^2 = (1/2-1)^2 = 1/4`

 

So the answers are;

`A = 1/2`

`B = -1`

`(A+B)^2 = 1/4`

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