What is int (2x^3-2x-3 ) / (-x^2+ 5 x )∫2x3−2x−3−x2+5x?

1 Answer
Bdub
Mar 17, 2016

int-2x-10-3/(5x)+237/(5(5-x)∫−2x−10−35x+2375(5−x)
=-x^2-10x-(3/5)lnx-(237/5)ln(5-x) +C=−x2−10x−(35)lnx−(2375)ln(5−x)+C

Explanation:

int(2x^3-2x-3)/(-x^2+5x)=int(-2x-10 +(48x-3)/(-x^2+5x ))∫2x3−2x−3−x2+5x=∫(−2x−10+48x−3−x2+5x)--->divide first

(48x-3)/(-x^2+5x) = A/x +B/(5-x) 48x−3−x2+5x=Ax+B5−x-->Partial Fractions

48x-3 = A(5-x)+Bx48x−3=A(5−x)+Bx

48x-3=5A-Ax+Bx->B-A=48,5A=-348x−3=5A−Ax+Bx→B−A=48,5A=−3

A=-3/5, B= 237/5A=−35,B=2375
int-2x-10-3/(5x)+237/(5(5-x)∫−2x−10−35x+2375(5−x)
=-x^2-10x-(3/5)lnx-(237/5)ln(5-x) +C=−x2−10x−(35)lnx−(2375)ln(5−x)+C

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