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KCET 2020 Math Solved Paper

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Question : 9 of 60

Marks: +1, -0

If

\int \frac{3x+1}{(x-1)(x-2)(x-3)} \, dx

= A \log |x-1| + B \log |x-2|

+ C \log |x-3| + C

, then the values of

A, B

C

are respectively,

$2,-7,5$
$5,-7,-5$
$2,-7,-5$
$5,-7,5$

Solution:

Let

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

= \frac{A}{x-1} + \frac{B}{x-2} + \frac{C}{x-3}

..... (1)

\int \frac{3x+1}{(x-1)(x-2)(x-3)} \, dx

= A \log |x-1| + B \log |x-2|

+ C \log |x-3| + C

Now,

3x + 1 = A(x-2)(x-3) + B(x-1)(x-3)

+ C(x-1)(x-2)

[From eqn.(1)]

Putting 𝑥 = 1, 𝑥 = 2, 𝑥 = 3 in the above equation one at a time, we get

𝐴 = 2, 𝐵 = −7, 𝐶 = 5

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