What is f(x) = int 1/(x-3)-x/(x+4) dxf(x)=∫1x−3−xx+4dx if f(-1)=6 f(−1)=6?

1 Answer
Alberto P.
Nov 9, 2016

f(x)=-x+lnabs(x-3)+4lnabs(x+4)+5-2ln2-4ln3f(x)=−x+ln|x−3|+4ln|x+4|+5−2ln2−4ln3

Explanation:

f(x)=lnabs(x-3)-int(y+4)/ydy + c = -y+4lnabsy+lnabs(x-3)+c=-x+4lnabs(x+4)+lnabs(x-3)+cf(x)=ln|x−3|−∫y+4ydy+c=−y+4ln|y|+ln|x−3|+c=−x+4ln|x+4|+ln|x−3|+c

Then

f(-1)= 6f(−1)=6 so

6=1+4ln3+ln4+c6=1+4ln3+ln4+c

c=5-4ln3-3ln2c=5−4ln3−3ln2

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