Integral Calculus Question 295
Question: $ \int_{{}}^{{}}{\frac{x^{2}+x-6}{(x-2)(x-1)}dx=} $
Options:
A) $ x+2\log (x-1)+c $
B) $ 2x+2\log (x-1)+c $
C) $ x+4\log (1-x)+c $
D) $ x+4\log (x-1)+c $
Show Answer
Answer:
Correct Answer: D
Solution:
$ \int_{{}}^{{}}{\frac{x^{2}+x-6}{(x-2)(x-1)},dx}=\int_{{}}^{{}}{\frac{(x+3)(x-2)}{(x-2)(x-1)},dx}=\int_{{}}^{{}}{\frac{x+3}{x-1},dx} $ $ =\int_{{}}^{{}}{\frac{x-1}{x-1},dx+\int_{{}}^{{}}{\frac{4}{x-1},dx}}=x+4\log (x-1)+c $ .
BETA
