Question

solve it fast plz......​

Answer 1

${\huge {\boxed {\red {\sf{AnSwEr}}}}}$

$━☞consider, \: I = \huge∫</p><p> \frac{(x - 1)(x - 2)(x - 3)}{(x - 4)(x - 5)(x - 6)} dx$

$━☞ I = \huge∫ I+ \frac{9 {x}^{2} - 63x + 114}{(x - 4)( - 5)(x - 6)} dx$

$━☞ let \: \frac{ {9x}^{2} - 63x + 114 }{(x - 4)(x - 5)(x - 6)} = \frac{A}{x - 4} + \frac{B}{x - 5} + \frac{C}{x - 6}$

$━☞ on \: solving \: the \: above \: eq. \: we \: get \: A = 3 ,B=-24,C=30$

$━☞\small{ Now, \: the \: integration \: reduces \: to;}$

$━☞ \huge∫ 1dx + \huge∫ \frac{3}{x - 4} dx + \huge∫ \frac{ - 24}{x - 5} dx + \huge∫ \frac{30}{x - 6} dx$

$━☞ x + 31n(x - 4) - 241n(x - 5) + 301n(x - 6)$