The value of -x-1x-2x-3x-4x-5x-6 dx iswhere -C- is the constant of integration

I=∫(x 1)(x 2)(x 3)(x 4)(x 5)(x 6)dx =∫[1+(x 1)(x 2)(x 3)(x 4)(x 5)(x 6) 1]dx =∫[1+(x 1)(x 2)(x 3) (x 4)(x 5)(x 6)(x 4)(x 5)(x 6)]dx =∫[1+3×2×1(x 4)( 1)( 2)+4×3× ...

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Byju's Answer

Standard XIII

Mathematics

Integration by Partial Fractions

The value of ...

Question

The value of $\int \frac{(x - 1) (x - 2) (x - 3)}{(x - 4) (x - 5) (x - 6)} d x$ is
(where $^{'} C^{'}$ is the constant of integration)

x + 3 ln | x - 4 | - 24 ln | x - 5 | + 30 ln | x - 6 | + C

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x + 3 ln | x - 4 | - 12 ln | x - 5 | + 30 ln | x - 6 | + C

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x + 3 ln | x - 4 | - 12 ln | x - 5 | + 36 ln | x - 6 | + C

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x + 12 ln | x - 4 | - 24 ln | x - 5 | + 30 ln | x - 6 | + C

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Solution

The correct option is A $x + 3 ln | x - 4 | - 24 ln | x - 5 | + 30 ln | x - 6 | + C$
$I = \int \frac{(x - 1) (x - 2) (x - 3)}{(x - 4) (x - 5) (x - 6)} d x$
$= \int [1 + \frac{(x - 1) (x - 2) (x - 3)}{(x - 4) (x - 5) (x - 6)} - 1] d x$
$= \int [1 + \frac{(x - 1) (x - 2) (x - 3) - (x - 4) (x - 5) (x - 6)}{(x - 4) (x - 5) (x - 6)}] d x$
$= \int [1 + \frac{3 \times 2 \times 1}{(x - 4) (- 1) (- 2)} + \frac{4 \times 3 \times 2}{(1) (x - 5) (- 1)} + \frac{5 \times 4 \times 3}{(2) (1) (x - 6)}] d x$
$= \int [1 + \frac{3}{(x - 4)} - \frac{24}{(x - 5)} + \frac{30}{(x - 6)}] d x$
$= x + 3 ln | x - 4 | - 24 ln | x - 5 | + 30 ln | x - 6 | + C$

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The value of ∫(x−1)(x−2)(x−3)(x−4)(x−5)(x−6) dx is (where ′C′ is the constant of integration)

The value of $\int \frac{(x - 1) (x - 2) (x - 3)}{(x - 4) (x - 5) (x - 6)} d x$ is
(where $^{'} C^{'}$ is the constant of integration)