_ ^ x^2 + x - 6 (x - 2)(x - 1) dx = - Vidyadip

MCQ

$\int_{}^{} {\frac{{{x^2} + x - 6}}{{(x - 2)(x - 1)}}dx = } $

A
$x + 2\log (x - 1) + c$
B
$2x + 2\log (x - 1) + c$
C
$x + 4\log (1 - x) + c$
✓
$x + 4\log (x - 1) + c$

✓

Answer

Correct option: D.

$x + 4\log (x - 1) + c$

d
(d)$\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$.

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