Question

(x +) a2-4)

Answer 1

The integral is given below as,

I= ∫ 5x ( x+1 )( x 2 −4 ) dx I= ∫ 5x ( x+1 )( x+2 )( x−2 ) dx

Use rule of partial fraction.

5x ( x+1 )( x+2 )( x−2 ) = A ( x+1 ) + B ( x+2 ) + C ( x−2 ) 5x=A( x 2 −4 )+B( x+1 )( x−2 )+C( x+1 )( x+2 )

Substitute x=2then,

C= 5 6

Substitute x=−1then,

A= 5 3

Substitute x=0then,

2A+B−C=0

Substitute and solve for B

B= −5 2

On integrating, we get

I= ∫ 5x ( x+1 )( x+2 )( x−2 ) dx = 5 3 ∫ dx x+1 − 5 2 ∫ dx x+2 + 5 6 ∫ dx x−2 = 5 3 log| x+1 |− 5 2 log| x+2 |+ 5 6 log| x−2 |+C