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If int(e^(x-1))/((x^2-5x+4))2xdx=A F(x-1...

If `int(e^(x-1))/((x^2-5x+4))2xdx=A F(x-1)+B F(x-4)+C` and `F(x)=int(e^x)/xdx ,t h e n`

A

`A= -2//3`

B

`B=(4//3)e^(3)`

C

`A=2//3`

D

`B=(8//3)e^(3)`

Text Solution

Verified by Experts

The correct Answer is:
A, D
`(2x)/((x-1)(x-4))=(C)/(x-1)+(D)/(x-4)`
`2x=C(x-4)+D(x-1)`
` :. C= -2//3, D=8//3`
` :. int(e^(x-1))/((x^(2)-5x+4))2xdx=int e^(x-1)((-2//3)/(x-1)+(8//3)/(x-4))dx`
`= -(2)/(3)F(x-1)+(8)/(3)e^(3)F(x-4)+C`
` :. A= -2//3, B=8//3e^(3)`
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