The value of -3x-1x-1x-2x-3dx iswhere m is an arbitrary constant

3x 1(x 1)(x 2)(x 3) = A(x 1)+B(x 2)+ C(x 3) ⇒ nbsp;3x 1 = A (x 2)(x 3)+ B(x 1)(x 3)+ C(x 1)(x 2)⋯ (1) By putting x=1; x=2 and x=3, we obtain A= 1, B= 5, C ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Antiderivative

The value of ...

Question

The value of $\int \frac{3 x - 1}{(x - 1) (x - 2) (x - 3)} d x$ is
(where $m$ is an arbitrary constant)

Open in App

Solution

$\frac{3 x - 1}{(x - 1) (x - 2) (x - 3)} = \frac{A}{(x - 1)} + \frac{B}{(x - 2)} + \frac{C}{(x - 3)} \Rightarrow 3 x - 1 = A (x - 2) (x - 3) + B (x - 1) (x - 3) + C (x - 1) (x - 2) \dots (1)$
By putting $x = 1; x = 2$ and $x = 3$ , we obtain
$A = 1, B = - 5, C = 4 ∴ \frac{3 x - 1}{(x - 1) (x + 2)} = \frac{1}{(x - 1)} - \frac{5}{(x - 2)} + \frac{4}{(x - 3)} \Rightarrow \int \frac{3 x - 1}{(x - 1) (x - 2) (x - 3)} d x = \int {\frac{1}{(x - 1)} - \frac{5}{(x - 2)} + \frac{4}{(x - 3)}} d x = ln | x - 1 | - 5 ln | x - 2 | + 4 ln | x - 3 | + m$
Where $m$ is an arbitrary constant.

Suggest Corrections

Similar questions

Q. The value of the integral

\int \frac{2 x}{(x^{2} + 1) (x^{2} + 3)} d x

is
(where

C

is an arbitrary constant)

Q. The value of the integral

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

is
(where

C

is an arbitrary constant)

Q. The value of the integral

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

is
(where

m

is an arbitrary constant)

Q. The value of the integral

\int \frac{1}{x^{4} - 1} d x

is
(where

C

is an arbitrary constant)

Q. The value of the integral

\int \frac{1 - x^{2}}{x (1 - 2 x)} d x

is
(where

C

is an arbitrary constant)

Join BYJU'S Learning Program

Explore more

Antiderivative

Standard XII Physics

Join BYJU'S Learning Program

The value of ∫3x−1(x−1)(x−2)(x−3)dx is (where m is an arbitrary constant)

The value of $\int \frac{3 x - 1}{(x - 1) (x - 2) (x - 3)} d x$ is
(where $m$ is an arbitrary constant)