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If int(1)/(x^(3)+x^(4))dx=(A)/(x^(2))+(...

If `int(1)/(x^(3)+x^(4))dx=(A)/(x^(2))+(B)/(x)+log|(x)/(x+1)|+C` , then

A

`A=(1)/(2), B=1`

B

`A=1, B=-(1)/(2)`

C

`A=-(1)/(2), B=1`

D

A = 1, B = 1

Text Solution

Verified by Experts

The correct Answer is:
C
`int(dx)/(x^(4)+x^(3))=int((x+1)-x)/(x^(3)(x+1))dx=int((1)/(x^(3))-(1)/(x^(2)(x+1)))dx`
`=int((1)/(x^(3))-(1)/(x^(2))+(1)/(x(x+1)))dx`
`=int((1)/(x^(3))-(1)/(x^(2))+(1)/(x)-(1)/(x+1))dx`
`=-(1)/(2x^(2))+(1)/(x)+log|x|-log|x+1|+C`
`-(1)/(2x^(2))+(1)/(x)+log|(x)/(x+1)|+C`
`therefore" "A=-(1)/(2) and B=1`
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