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What is #int (2x^3-2x-3 ) / (-x^2+ 5 x )#?

Answer 1

Ezekiel Alexander

#int-2x-10-3/(5x)+237/(5(5-x)#
#=-x^2-10x-(3/5)lnx-(237/5)ln(5-x) +C#

#int(2x^3-2x-3)/(-x^2+5x)=int(-2x-10 +(48x-3)/(-x^2+5x ))#--->divide first

#(48x-3)/(-x^2+5x) = A/x +B/(5-x) #-->Partial Fractions

#48x-3 = A(5-x)+Bx#

#48x-3=5A-Ax+Bx->B-A=48,5A=-3#

#A=-3/5, B= 237/5# #int-2x-10-3/(5x)+237/(5(5-x)# #=-x^2-10x-(3/5)lnx-(237/5)ln(5-x) +C#

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Answer 2

Samantha Adkison

To find the quotient of the given polynomials, perform polynomial long division or synthetic division. Here's the solution:

   2x - 2   
___________

x^2 - 5x | 2x^3 + 0x^2 - 2x - 3 - (2x^3 - 10x^2) ________________ 10x^2 - 2x - 3 - (10x^2 - 50x) _______________ 48x - 3

So, the quotient is 2x - 2 with a remainder of 48x - 3.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.