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Integrate : $\int \large\frac{3x}{(x+1)(x+2)}$$dx$

$(a)\;6 \log (x+2)-3 \log (x+1)+c \\(b)\;-3\log (x+1)+c \\(c)\; 6 \log 2- 3 \log (x+1) \\ (d)\;None$

1 Answer

$\int \large\frac{3x}{(x+1)(x+2)}$$dx$
first find x value in denominator,
Put x value in denominator and numerator and do put value of x, where infinite condition occured so,
$\int \large\frac{3(-2)}{(-2+1)(x+2)}$$dx+\int \large\frac{3(-1)}{(x-1)(-1+2)}$
$\qquad= \int \large\frac{6}{(x+1)}$$dx-\int \large\frac{3}{x+1}$$dx$
$6 \log (x+2)-3 \log (x+1)+c$
Hence a is the correct answer.
answered Dec 31, 2013 by meena.p