Question

integration of dx/(x-ax²)​

Answer 1

$\huge\pink{\boxed{\blue{\boxed{ \purple{ \boxed{{\pink{Answer}}}}}}}} \\ \large\pink{\boxed{\blue{\boxed{ \purple{ \boxed{{\pink{Your~answer↓}}}}}}}} \\ \large\bold\red{question \: based \: on \: integration}$

$∫  \frac{dx}{x - {ax}^{2} } \\ = - \frac{1}{a} ∫  \frac{dx}{ {x}^{2} - \frac{1}{a} x} \\ \small\bold\red{(using \: completing \: squares \: method)}\\ = - \frac{1}{a} ∫  \frac{dx}{ {x}^{2} - \frac{1}{a} x + \frac{1}{ {4a}^{2} } - \frac{1}{ {4a}^{2} } } \\ = - \frac{1}{a} ∫  \frac{dx}{ {(x - \frac{1}{2a} )}^{2} - {( \frac{1}{2a} )}^{2} } \\ = - \frac{1}{a} \times \frac{1}{2 \times \frac{1}{2a} } log( \frac{x - \frac{1}{2a} - \frac{1}{2a} }{x - \frac{1}{2a} + \frac{1}{2a} } ) + c \\ = - log( \frac{x - a}{x} ) + c\\ = log( \frac{x}{x - a} ) + c$

$\small\bold\red{formula \: used} \\ \small\bold\red{ ∫  \frac{dx}{ {x}^{2} - {a}^{2} } = \frac{1}{2a} log( \frac{x - a}{x + a} ) + c}$

$\huge \fcolorbox{black}{cyan}{♛hope \: it \: helps \: you♛}$