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int(x^(2)-1)/(xsqrt(x^(4)+3x^(2)+1))dx=...

`int(x^(2)-1)/(xsqrt(x^(4)+3x^(2)+1))dx=`

A

`log_(e)|x+(1)/(x)+sqrt(x^(2)+(1)/(x^(2))+3)|+C`

B

`log_(e)|x-(1)/(x)+sqrt(x^(2)+(1)/(x^(2))-3)|+C`

C

`log_(e)|x+sqrt(x^(2)+3)|+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
a
We have , `I=int(x^(2)-1)/(sqrt(x^(4)+3x^(2)+1))dx=int(1-(1)/(x^(2)))/(sqrt(x^(2)+3+(1)/(x^(2))))dx`
`rArrI=int(1)/(sqrt((x+(1)/(x))^(2)+1^(2)))d(x+(1)/(x))`
`rArrI=log_(e)|x+(1)/(x)+sqrt((x+(1)/(x))^(2)+1)|+C`
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OBJECTIVE RD SHARMA ENGLISH-INDEFINITE INTEGRALS-Solved Example
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