Question

Evaluate the improper integral
dt/( t^2-2t)

Answer 1

(dt)/(t^(2)-2t)

Factor out the GCF of t from each term in the polynomial.
(dt)/(t(t)+t(-2))

Factor out the GCF of t from t^(2)-2t.
(dt)/(t(t-2))

Reduce the expression (dt)/(t(t-2)) by removing a factor of t from the numerator and denominator.
(d)/(t-2)

Answer 2

... separate using partial fraction then integrate easily

Answer 3

dt/(t^2-2t)=dt/t(t-2)=A/t +B/(t-2)
now (At-2A+Bt)/t(t-2).
by compairing it gives -2A=1 or A=-1/2.
A+B=0 so B=1/2
now put the value of A and B.
the function become....(-1/2)/t +(1/2)/(t-2)
-1/2 log t +1/2 log t-2
log {squareroot of (t-2)/t} +c