$\int \frac{(x - 1) (x - 2) (x - 3)}{(x - 4) (x - 5) (x - 6)}$
find coeficent of partial fraction

Open in App

Solution

$I = \int \frac{(x - 1) (x - 2) (x - 3)}{(x - 4) (x - 5) (x - 6)} d x$
$\frac{(x - 1) (x - 2) (x - 3)}{(x - 4) (x - 5) (x - 6)} = \frac{A}{x - 4} + \frac{B}{x - 5} + \frac{C}{x - 6}$
$(x - 1) (x - 2) (x - 3) = A (x - 5) (x - 6) + B (x - 4) (x - 6) + C (x - 4) (x - 5)$
Put $x = 5$
$4 \times 3 \times 2 = B (1) (- 1)$
$24 = - B$
$B = - 24$
Put $x = 6$
$5 \times 4 \times 3 = c (2) (1)$
$c = 30$
Put $x = 4$
$3 \times 2 \times 1 = A (- 1) (- 2)$
$6 = 2 A$
$A = 3$

Suggest Corrections

Similar questions

\int \frac{(x - 1) (x - 2) (x - 3)}{(x - 4) (x - 5) (x - 6)} d x

\frac{5 x - 11}{2 x^{2} + x - 6}

\frac{5 x^{2} - 4 x^{2} + 3}{(x - 2)^{2} (x + 1)}

\frac{2 x + 1}{(3 x + 2) (4 x^{2} + 5 x + 6)}

\frac{2 x^{2} + 5 x - 11}{x^{2} + 2 x - 3}

Join BYJU'S Learning Program