Question

integrate. x²+2/(x-1)(x+2)(x+3)​

Answer 1

$\begin{gathered} {x}^{2} + \frac{1}{ {x}^{2} } - 2 - 3x + \frac{1}{3x} \\ \\ \\ = {x}^{2} + \frac{1}{ {x}^{2} } - 2(x \times \frac{1}{x} ) - 3(x - \frac{1}{x} ) \\ \\ \\ = > {(x - \frac{1}{x}) }^{2} - 3(x - \frac{1}{x} ) \\ \\ \\ = > (x - \frac{1}{x} )(x - \frac{1}{x} - 3)\end{gathered}$

$x2</p><p> + </p><p>x </p><p>2</p><p> </p><p>1</p><p> </p><p> −2−3x+ </p><p>3x</p><p>1</p><p> </p><p> </p><p>=x </p><p>2</p><p> + </p><p>x </p><p>2</p><p> </p><p>1</p><p> </p><p> −2(x× </p><p>x</p><p>1</p><p> </p><p> )−3(x− </p><p>x</p><p>1</p><p> </p><p> ) \\ </p><p>=>(x− </p><p>x</p><p>1</p><p> </p><p> ) </p><p>2</p><p> −3(x− </p><p>x</p><p>1</p><p> </p><p> ) \\ </p><p>=>(x− </p><p>x</p><p>1</p><p> </p><p> )(x− </p><p>x</p><p>1</p><p> </p><p> −3)$