Two Antiderivatives (VCE SSCE Mathematical Methods): Quizzes

$\frac{1}{a(r+1)}(ax+b)^{r+1} + c$

$r = -1$

$\frac{1}{a}\log_e|ax+b| + c$

$\frac{1}{18}(3x+1)^6 + c$

It would involve division by zero

$\frac{2}{3}\log_e|3x-2| + c$

It avoids separate positive/negative cases

Increase power by 1, divide by $a(r+1)$

$-\frac{2}{3}\log_e|2-3x| + c$

Constant of integration $c$