Question

求积分 x* dx/ (x+1)(x-2)

Answer 1

x/(x+1)(x-2)

=a/(x+1)+b/(x-2)

=(ax-2a+bx+b)/(x+1)(x-2)

x=ax-2a+bx+b

所以a+b=1

-2a+b=0

a=1/3,b=2/3

原式=∫1/3*1/(x+1)dx+∫2/3*1/(x-2)dx

=1/3*ln|x+1|+2/3*ln|x-2|+C