Question

$\int \frac{x^2+x-1}{x^2+x-6}dx=$

• A. $x+\log p+5|+\log |x-2|+c$
• B. $x-\log |x+3|+\log |x-2|+c$
• C. $x-\log |x+3|-\log |x-2|+c$
• D. None of these

Answer 1

The correct option is B $x-\log |x+3|+\log |x-2|+c$

$\int \frac{x^2+x-1}{x^2+x-6}dx=?$

$=\int \frac{x^2+x-1}{(x+3)(x-2)}dx$

$=\int (1+\frac{5}{(x+3)(x-2)})dx$

$=\int 1dx+\frac{5}{5}\int [\frac{1}{x-2}-\frac{1}{x+3}]dx$

$=x+log(x-2)-log(x+3)+c$

$=x-log(x+3)+log(x-2)+c$

Option (b)