What is f(x) = int 1/(x+3)-1/(x-2) dxf(x)=∫1x+3−1x−2dx if f(-1)=3 f(−1)=3?

1 Answer
Ananda Dasgupta
Apr 3, 2018

f(x)=ln|3/2 (x+3)/(x-2)|+3f(x)=ln∣∣∣32x+3x−2∣∣∣+3

Explanation:

f(x) = int [1/(x+3)-1/(x-2)] dx = ln|x+3|-ln|x-2|+Cf(x)=∫[1x+3−1x−2]dx=ln|x+3|−ln|x−2|+C
qquad = ln|(x+3)/(x-2)|+C

Since f(-1) = 3, we have

3 = ln|(-1+3)/(-1-2)|+C = ln|-2/3|+C implies C = 3-ln|2/3|

Thus

f(x) = ln|(x+3)/(x-2)|+3-ln|2/3|=ln|3/2 (x+3)/(x-2)|+3

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