Question

Resolvex+2/(1-x2) (x2+1)into Partial fractions​

Answer 1

Answer:

Step-by-step explanation:

We need to find  

A

,

B

,

C

such that

1

x

2

(

2

x

−

1

)

=

A

x

+

B

x

2

+

C

2

x

−

1

for all  

x

.

Multiply both sides by  

x

2

(

2

x

−

1

)

to get

1

=

A

x

(

2

x

−

1

)

+

B

(

2

x

−

1

)

+

C

x

2

1

=

2

A

x

2

−

A

x

+

2

B

x

−

B

+

C

x

2

1

=

(

2

A

+

C

)

x

2

+

(

2

B

−

A

)

x

−

B

Equating coefficients give us

⎧

⎪

⎨

⎪

⎩

2

A

+

C

=

0

2

B

−

A

=

0

−

B

=

1

And thus we have  

A

=

−

2

,

B

=

−

1

,

C

=

4

. Substituting this in the initial equation, we get

1

x

2

(

2

x

−

1

)

=

4

2

x

−

1

−

2

x

−

1

x

2

Now, integrate it term by term

∫

 

4

2

x

−

1

 

d

x

−

∫

 

2

x

 

d

x

−

∫

 

1

x

2

 

d

x

to get

2

ln

|

2

x

−

1

|

−

2

ln

|

x

|

+