Integral Calculus Question 27
Question: $ \int_{{}}^{{}}{\frac{x^{2}+x-1}{x^{2}+x-6}\ dx=} $
[AISSE 1988]
Options:
A) $x+\log \left|(x+3)\right| +\log \left| (x-2)\right|+C$
B) $x-\log \left|(x+3)\right|+\log \left| (x-2)\right|+C$
C) $x-\log \left|(x+3)\right|-\log \left| (x-2)\right|+C$
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ \int_{{}}^{{}}{\frac{x^{2}+x-1}{x^{2}+x-6},dx}=\int_{{}}^{{}}{[ 1+\frac{5}{x^{2}+x-6} ]},dx $ $ =\int_{{}}^{{}}{[ 1+\frac{5}{(x+3)(x-2)} ]},dx $ $ =\int_{{}}^{{}}{dx}+\int_{{}}^{{}}{\frac{dx}{x-2}}-\int_{{}}^{{}}{\frac{dx}{x+3}} $ $ =x+\log (x-2)-\log (x+3)+c $ .
BETA
